pc iv: molecular spectroscopy / molekülspektroskopie prof

PC IV MOLECULAR SPECTROSCOPY

Molekuumllspektroskopie

Prof Oleg Vasyutinskii and Prof Karl-Heinz Gericke

Summer Semester from April 2 2009 till July 10 2009

Lectures Thursday 800 ndash 930 (PK112)Friday 1130 ndash 1215 (PK112)

Exercises Friday 1215 ndash 1300 (PK112)

What is Spectroscopy

The study of molecularstructure and dynamics throughthe absorption emission and

scattering of light

URL Internet Skript

Vorlesung httpwwwpcitu-bsdeaggerickePC4Englisch httpwwwpcitu-bsdeaggerickePC4eDownload httpwwwpcitu-bsdeaggerickePC4edownload

Exercises httpwwwpcitu-bsdeaggerickePC4eexercises

List of References

bullBanwell Colin N McCash Elaine M ldquoFundamentals of Molecular SpectroscopyTata McGraw Hill ISBN 0074620258

bullHaken Wolf ldquoMolekuumllphysik und Quantenchemierdquo Springer ISBN 3-540-5

bullP W Atkins ldquoPhysical Chemistryrdquo or ldquoPhysikalische Chemierdquo

bullKettle ldquoSymmetrie und Strukturrdquo Teubner Taschenbuch

bullW Kutzelnigg ldquoEinfuumlhrung in die Theoretische Chemierdquo Band I II VerladChemie ISBN 3-527-25719-9

bullR McWeeny ldquoCoulsons Chemische Bindungrdquo SHirtzel-Verlag Stuttgart ISBN 3-7776-0383-x

bullB Webster ldquoChemical Bonding Theoryrdquo Bleckwell Scientific Publications ISBN 0-632-01619-1 (-01621-3)

bullD A Quarrie ldquoQuantum Chemistryrdquo Oxford University Press

bullG Wedler ldquoLerbuch der Physikalischen Chemierdquo 4 Auflage VCH 1997 ISBN 3-527-29481-3

bullG Herzberg ldquoMolecular Spectra and Molecular Structurerdquo V I II III Princeton

Spectrum of Electromagnetic Waves

Visible Light

Spectral Areas

700 600 500 400

Wavelength nm

ν = сλ (Hz)

Electromagnetic Spectrum

Type of Radiation

Frequency Range (Hz)

Wavelength Range Type of Transition

gamma-rays 1020-1024 lt1 pm nuclear

X-rays 1017-1020 1 nm-1 pm inner electron

ultraviolet 1015-1017 400 nm-1 nm outer electron

visible 4-75x1014 750 nm-400 nm outer electron

near-infrared 1x1014-4x1014 25 microm-750 nm outer electron molecular vibrations

infrared 1013-1014 25 microm-25 microm molecular vibrations

microwaves 3x1011-1013 1 mm-25 microm molecular rotations electron spin flips EPR

radio waves lt3x1011 gt1 mm nuclear spin flips NMR

Electromagnetic Radiation

Light Polarization

E

Circularly polarized light

Unpolarized light

E

Linearly polarized light

Linear Polarization

A plane electromagnetic wave is said to belinearly polarized The transverse electricfield wave is accompanied by a magneticfield wave as illustrated

Circular Polarization

Circularly polarized light consists of twoperpendicular electromagnetic plane waves of equal amplitude and 90degdifference in phase The light illustratedis right- circularly polarized

How to produce polarized light

3 Crystal polarizers (Glan Prism)

Brewsterrsquos angle

=

1

2arctannn

Bθ

n1

n2p-polarization

where n1 and n2 are refraction indices

For the pair air (n1=1) ndash glass (n2= 15) for visible light θB asymp 56o Stack of glass plates can be used as a polarizer for transmitted light

s-polarization

1 Reflection from a surface or refraction through a plate

2 Dichroic polaroids (thin films)

Optical transitions occurring due to the radiation-matter interaction

The integration absorption coefficient Transitions

dN2dt = B12

u(ν) N1dN

2dt = ndash B21 u(ν) N2

dN2dt = ndash A21 N2

A21 B12 = 8πh ν sup3csup3B21 B12 = g2 g1

Einstein Coefficients

Albert Einstein 14 Maumlrz 1879 in Ulm Wuumlrttemberg+ 18 April 1955 in Princeton New Jersey USANobel Prize 1921 fuumlr Photoeffekt

He developed the Theory of Photoeffect the Theory of Light Absorption myMatter the Special Relativistic Theory and the General Ralativistic Theory

Albert Einstein

Lambert-Beer LawTransmittance of the sample

T = I I0 T = e-σNl = e-α

where ε [L mol-1 cm-1] is the extinction coefficient and c [mol L-1] is the molar concentration

The form which widely used in laboratory practice

T = 10-εcl

where σ [cm2] is an absorption cross section N[cm-3] is a concentration andl [cm] is a sample length

NA is Avogadro number NA = 6022 10-23 mol-1

AA NN

VNmoleculesofNumberC ==

Low Optical Density Approximation

In case if the exponent factor α = σ N l is small compared to unity αltlt 1 the exponential function can be expanded over α Keeping in this expansion only first two terms one comes to the important for practice particular case calledlow optical density of the sample

I = I0(1 - σ N l)

Integrating the cross section σ = σ(ν) over the light frequency ν within theabsorption peak one obtains the integrated cross section ltσ(ν)gt

where B12 is the Einstein absorption coefficient and ν0 is the center of the molecular absorption line Thus the Einstein coefficient B12 can be directlydetermined from experiment

chBd 0

12)( νννσσ == int

Spectral Line ShapeUncertainty relation for energy

Two main processes which are responsible to the finite lifetime of excited states

1 Spontaneous decay which is proportional to the corresponding Einstein coefficient Anm The intensity of the spontaneous decay is proportional to the square of the matrixelement of the interaction of the molecule with electromagnetic modes of vacuum

2 Interaction between the molecular quantum states and other particles and fields In the gas phase this interaction is mostly inelastic collisions with surrounding particles In the condensed matter there can be interaction with phonons (vibration of the surrounding lattice)

The corresponding line has the Lorentz shape

where γ = 12πτ is the decay rate

and ∆νL = γ

τh

asymp∆E

( )2

20 2

21)(

+minus

=γ

γ

πν

vvI

Homogeneous (Lorentz) Broadening

Condition ∆νL (Hz) ∆νL (cm-1)

Natural lifetimes Gas phase electronic transitions

sim 107 sim 10-4

Natural lifetimes Gas phase rotational transitions

sim10-4 sim 10-15

Collisionallifetimes

Gas atmospheric pressure

sim 109 sim 10-2


Liquid electronic transitions

sim 1012 sim 101

Inhomogeneous BroadeningThe Doppler effect results in the shift of the light frequency when a light source is moving toward or away (+-) from an observer When the source emits radiation with a frequency ν0 and moves with a velocity v the observer detects the light frequency

plusmn=

cZ

0v1νν

Molecules in a gas move chaotically in all directions In case of thermal equilibrium the distribution of the molecular velocities along the line of detection (z axis) is known as the (1-dimensional) Maxwell-Boltzmann distribution

minus=

Tkm

kTmf

2vexp

2)v(

2Z

Z π

The observer detects the corresponding Doppler-broadened spectral line profile

( )

∆minus

minus∆

= 2

202ln4exp12ln4)(

DD

Iννν

νπν where

mTk

cD2ln22 0ν

ν =∆

For transitions which belong to the visible or near-UV spectral range the Doppler width is typically within one GHz at temperature around 300 K For this spectral range the Doppler line broadening is usually much larger than the lifetime (Lorentz-type) broadening

Lorentz and Doppler Line Shapes

Experiment with particles

P12 = P1 + P2

de Broglie a Particle is a Wave

Wavelength λ = hmv

Louis Victor Pierre Raymond duc de Broglie 15 Aug 1892 in Dieppe France+ 19 Maumlrz 1987 in Paris France

Nobelpreis 1929

De Broglies Dissertation ldquoRecherches sur la theacuteorie des quantaldquo in 1924 at the firts time gave a relationship between a particle massm its velocity v and the correspondingwavelength λ

Interference of Matter Waves

φ = A eminusiωt+ikx

ω=2π Εh Frequency

k = 2πλ = ph Wavevector

Probability to detect the particleI = |φ|2

φ = φ1+φ2I = |φ1+φ2|2

I = I1+I2+2(I1I2)frac12cos ∆ϕ

where ∆ϕ is the phase difference

The Schroumldinger EquationTime-independent Schroumldinger Equation

[minus hsup22mdsup2dxsup2 + V(x)] ψ(x) = E ψ(x) (1 dimension)

[minus hsup22m ∆ + V(xyz)] ψ(xyz) = E ψ(xyz) (3 dimensions)

where ∆ is the Laplace operator ∆ = partsup2partxsup2 + partsup2partysup2 + partsup2partzsup2

Time-dependent Schroumldinger Equation

[minus hsup22mpartsup2partxsup2 + V] ψ(xt) = ih partpartt ψ(xt)

minusinfinint+infin|ψ(xyz)|2 dx dy dz = 1

Normalization of the wave function

Calculation of the Probability Amplitude (Wavefunction)

There are three mathematicallyequivalent ways for calculating theprobability amplitude1) Matrix algebra

Werner HeisenbergNobelpreis 1932

2) Differential equation DGLErwin SchroumldingerNobelpreis 1933

3) Trajectory integralsRichard Feynman Nobelpreis 1965

12 Aug 1887 in Erdberg Wien+ 4 Jan 1961 in Wien

11 Mai 1918 in Far Rockaway New York+ 15 Feb 1988 in Los Angeles

5 Dez 1901+ 1 Feb 1976

Hydrogen Atom

reZ

mH e

e 0

22

2

42 επminusnablaminus=

h

2

2

2

2

2

22

zyxe partpart

+partpart

+partpart

=nabla ( )φθ 1 222

2 Λ+

partpart

partpart

=nablar

rrre

( )θ

θθθθθ

φθpartpart

partpart

+partpart

=Λ sinsin

1sin

1 2

2

22

Hamiltonian

Wavefunctions

-

+

)( φθψ rk where k equiv n l s ml ms

sl msmlnlk rRr χφθφθψ )()()( Υ=

Rn l are Associated Laguerre Polynomials and Yl m are Spherical Harmonics

Polar coordinates

kkk EH ψψ =

Hydrogen Atom Wavefunctions Radial Part

230

10

02aeR

ar

minus

=

230

2

020 22

2 0

a

ear

R

ar

minus

minus

= 230

2

021 62

0

a

ear

R

ar

minus

=

Spherical Harmonics l = 0 1 2 3 4

Ylm(θ φ) = Plm(cos θ) fm (φ) fm (j) = 1(2π)frac12 eimφ

Eleсtron l m Ylm(θ φ) |Ylm|2

s 0 0 1(4 π)frac12 14 π

p11

plusmn10

iexcl(38 π)frac12 sin θ eplusmniφ

(34 π)frac12 cos θ

38 π sinsup2 θ34 π cossup2 θ

d222

plusmn2plusmn10

(1532 π)frac12 sinsup2 θ eplusmn2iφ

iexcl(158 π)frac12 sin θ cos θ eplusmniφ

(516 π)frac12 (3cossup2 θ -1)

1532 π sin4 θ158 π sinsup2 θ cossup2 θ516 π(3cossup2 θ -1)sup2

f

3333

plusmn3plusmn2plusmn10

iexcl(3564 π)frac12 sin3 θ eplusmn 3i φ(10532 π)frac12 sinsup2 θ cos θ eplusmn2iφ

iexcl(2164 π)frac12 sin θ (5 cossup2 θ - 1) eplusmniφ

(716 π)frac12 (5 cos3 θ - 3 cos θ)

3564 π sin6 θ10532 π sin4 θ cossup2 θ

2164 π sinsup2 θ (5 cossup2 θ - 1)sup2716 π (5 cos3 θ - 3 cos θ)

g

44444

plusmn4plusmn3plusmn2plusmn10

(315512 π)frac12 sin4 θ eplusmni4φ

iexcl(31564 π)frac12 sin3 θ cos θ eplusmn3iφ

(225660 π)frac12 sinsup2 θ (7 cossup2 θ - 1) eplusmn2iφ

iexcl(225320 π)frac12 sin θ (7cos3 θ -3cosθ) eplusmniφ

(9256 π)frac12 (35 cos4 θ - 30 cossup2 θ + 3)


225660 π sin4 θ (7 cos3 θ - 1)sup2225320 π sinsup2 θ (7 cos3 θ - 3 cos θ)sup29256 π (35 cos4 θ - 30 cossup2 θ + 3)sup2

Real wave functions (linear combinations)

dxy = ndash iradic2 (Y22 ndash Y2-2 ) = (1516π)frac12sinsup2θsin2φ

dxsup2-ysup2 = 1radic2 (Y22 + Y2-2 ) = (1516π)frac12 sinsup2θ cos2φ

dyz = iradic2 (Y21 + Y2-1 ) = (154π)frac12 sinθ cosθ sinφ

dxz = -1radic2 (Y21 ndash Y2-1 ) = (154π)frac12 sinθ cosθ cosφ

d3zsup2-rsup2 = Y20 = (516π)frac12 (3 cossup2θ - 1)0

1

2

2

py = iradic2 (Y11 + Y1-1 ) = (34π)frac12 sinθ sinφ

px = -1radic2 (Y11 ndash Y1-1 ) = (34π)frac12 sinθ cosφ

pz = Y10 = (34π)frac12 cosθ0

11

s = 1(4p)frac1200

Wave Functions|ml|l

Hydrogen Atom Wavefunctions Angular Part pX orbital pY orbital

l = 1 m = plusmn1s orbital

l = 0 m = 0

l = 2

pZ orbitall = 1 m = 0

dzsup2 orbital m=0 dxsup2-ysup2 orbital

dxy orbital dzx orbital dyz orbital

Niels Henrik David Bohr

7 Okt 1885 in Kopenhagen + 18 Nov 1962 in Kopenhagen

Nobelpreis 1965

Hydrogen Atom Energy Levels

K32124

12

0

2

0

=minus= nna

eEnl πε

ε0 is the Vacuum permittivity ε0 = 8854middot10-12 J-1 C2 m-1

e is the Elementary charge e = 1602middot10-19 Ca0 is the Bohr radius a0 = 4πε0ħ2mee2 = 5292middot10-11 m

Selection rules for radiative transitionsl ndash l = plusmn1 ml ndash ml = 0 plusmn1

s - s = 0 ms ndash ms = 0

Selection rules for radiative transitionsj ndash j = 0 plusmn1 mj ndash mj = 0 plusmn1

Spin-orbital interaction in Hydrogen atom

j = l + s

l s

j = l ndash frac12

j = l + frac12

2

4

3

42

21

)1( h

mellnZE jj +

=∆ primeprimeprimeα

α asymp 1137 - fine structure constantFor n = 2 3 и 4 0440120360=∆ primeprimeprimejjE cm-1

Electron spin magnetic moment

z-projection

Electron orbital magnetic moment

z-projection

where μB is the Bohr magneton

TJ

me

eB

24102792

minussdot==h

micro

sBsZ

Bs

lBlZ

Bl

msm

l

micromicromicromicromicromicro

micromicro

22minus=

minus=minus=

minus=

rr

rr

Multi-electron atoms1 Each electron moves in the field of atomic nucleous and all other electrons This field is named the Self-Consistent Field The Self-Consistent field is spherically symmetric however it is not a Coulomb field The corresponding Schroumldinger equation cannot be solved analytically Approximate wave functions and atomic energy levels for each electron can be obtained by computing the set of Hartree-Fock differential equations

2 The obtained one-electron energy levels depend on the quantum numbers n и l These energy levels are filled by all electrons which form the electron configuration of an atom The filling of the energy levels if performed following the Pauli Principle

Two electrons cannot simultaneously occupy the state with the same quantum numbers

Therefore each s-state (l = 0) can be populated with no more than two electrons each p- state (l = 1) can be populated with no more than six electrons each d- state (l = 2) can be populated with no more than ten electrons and so on

3 The quantum numbers which describe a quantum state of the whole multielectron atom can be obtained by summation the moments of individual electrons using the quantum mechanical rules

L ndash total orbital angular momentum of the atom МL ndash projection of L onto the direction ZS ndash total electron spin MS ndash projection of S onto the direction ZJ ndash total electron angular momentum J = L + S MJ ndash projection of J onto the direction Z P = (-1)Σ li = plusmn 1 ndash atomic parity

Wolfgang Ernst Pauli

25 April 1900 in Wien+ 15 Dez 1958 in Zuumlrich

Nobelpreis 1945

The nomenclature of the energy levels (terms) inmultielectron atoms in the LS approximation

L ndash L МL ndash МL S ndash S MS ndash MS J ndash J MJ ndash MJ P

0 plusmn 1 0 plusmn 1 0 0 0 plusmn 1 0 plusmn 1 + harr ndash

Selection rules for radiative transitions in multielectron atoms

JS L12 +

oJ

S L12 +

- even states

- odd states

J + J ge 1

S = 1 Triplet state

L = 0 S -state

L = 2 D -state

S = 0 Singlet state

L = 1 P -state

Physical meaning of the selection rules for the quantum number М

ΔM = 0 plusmn1

M = ndash1

J = 1

J = 0

M = 0

M = 1M = 0

Z

e perp Ze perp Z

e Z

e

ΔM = ndash 1

ΔM=0

ΔM=plusmn1

ΔM = 1

In the absence of external fields all М-sublevels at fixed J-value are degenerated

The fine structure of spectral linesThe fine structure is a result of the spin-orbit interaction

L S

Jmin = |L ndash S|

Jmax = L + SJ+1J

L S

Jmin = |L ndash S|

Jmax = L + SJ+1J

VSO = A LS

EJ = frac12 A [ J (J+1) ndash S(S+1) ndash L(L+1)] rarr ΔEJ J-1 = A J

This is the Lande interval rule

А gt 0

А gt 0

The hyperfine structure of spectral linesThe hyperfine structure of spectral lines is a results of interaction between the

dipole and quadrupole moments of nuclei with electrons

J I

Fmin = |J ndash I|

Fmax = J + IF+1F

J I

Fmin = |J ndash I|

Fmax = J + IF+1F

Vhpf = AI JI

EF = frac12 AI [ F(F+1) - J (J+1) - I(I+1)] rarr ΔEF F-1 = AI F

Lande interval rule

μ = μn gI IgI is the nuclear gyromagnetic ratioμn is the nuclear magneton

Nuclear electric quadrupole moment

Nuclear magnetic dipole moment

Qαβ = Σi ei (3riαriβ ndash δαβ ri2)

Q = ltγ I MI|QZZ| γ I MI gtM=I

sum partpartpart

+minus=+=βα βα

αβmicroϕ

micro

2

6)0(

xxQeHWWW Q

F = J + I

The full Hamiltonian H = H0 + V where H0 raquo VThe exact solution for the non-perturbed We seek for an approximate solutionquantum problem is known for the full Hamiltonian Н

H0 ψn(0) = E(0) ψn

(0) (H0 + V) ψ = E ψwhere ψn

(0) is the non-perturbed wave function

A little-bit of quantum mechanics Perturbation theory for nondegenerate quantum states

1 The perturbed wave function is presented as an expansion over the unperturbed wave functions

2 This expansion is substituted into the Schroumldinger equation for the full Hamiltonian

3 The obtained expression is multiplied from the left by Ψk

(0)(q) and integrated over all coordinates q

4 Using the orthogonality of the wave function we obtain the first approximation correction for the k ndash level energy

sum=n

nn qcq )()( )0(ψψ

int == )0()0()0()0()1( )()( kkkkk VdqqVqE ψψψψ

The perturbation theory for non-degenerate quantum statesSecond-order approximation

5 Substituting the obtained first-order solution again the Schroumldinger equation we can get the expression for the second-approximation correction to the k ndash th level energy

kmEE

kVmmVkE

m mkk ne

minus= sum )2(

In general Еk = Еk(0) + Ek

(1) + Ek(2) + hellip

The Hamiltonian H = H0 + V

The exact solution for the non-perturbed We seek for an approximate solutionwave function is for the full Hamiltonian H

H0 ψn(0) = E(0) ψn

(0) (H0 + V) ψ = E ψwhere E(0)

n = E(0)n

The perturbation theory for degenerate quantum states

sum Ψ=Ψn

nn qcq )()( )0()0()0(

1 The wave function in the zero approximation Ψ(0)(q) is sought as an expansion over the wave functions Ψn

(0)(q)

2 This expansion is substituted to the Schroumldinger equationfor the full Hamiltonian

3 The obtained expression is multiplies from the right on Ψnrsquo(0)(q)

and integrated over all coordinates q

4 The solution of the obtained set of algebraic equations gives the energy corrections of the 1st approximation En and the expansion coefficients c(0)

n

( )sumprime

prime =minusn

nnnn cEnVn 0 )0(δThe set of N linear equations for

determination of the expansion coefficients c(0)

n and the energy corrections En

This determinant must be equal to zero which allows for determination of the 1st

approximation energy corrections En

The determinant is equivalent to the Nth ndashorderalgebraic equation on the variable Е which is called Secular Equation

0

21

22221

11211

=

minus

minusminus

EVVV

VEVVVVEV

NNNN

N

N

L

LLLL

L

L


An atom in an external electric field Stark effect

WE = - E D = e E Σi ri

sumprimeprime primeprimeminus

primeprimeprimeprime+minus=∆

J JJ

ZZZMJ EE

MJDMJMJDMJMJDMJE

γ γγγ

γγγγγγ 2EE

0 ΔEγJM = E 2 [ AγJ + BγJ M2 ]After applying a homogeneous external electric field the energy level | γ J M gt is splittedinto the components which refer to the quantum numbers

|M| = J J-1 hellipIn case of strong electric field when the Stark shifts are comparable with the initial splitting between the energylevels |γ J gt |γ J gt the expression for the total energy splitting is written as

22

21 2MJDMJE Z primeprime+

∆

plusmn=∆ γγ2E

Thus for large fields the initially quadratic Stark effect becomes linear

Fluorescence polarization due to the Stark effect

M = ndash1

Jrsquo = 1

Jrsquorsquo = 0

M = 0

M = 1

M = 0

e perp Ze perp Z

e Z

ΔM=0

ΔM=plusmn1

σ - component

π - component

σ - component

Z E e

Observing the fluorescence from the state Jrsquo=1 to the state Jrsquorsquo=0 along the electric field direction one can see a single spectral line (σ ndash component) while observing the fluorescence perpendicular to the electric field direction one can see two close spectral lines (σ ndash and π ndash components)

An atom in an external magnetic field Zeeman effect

EB = lt WB gt = g μB B M

μ = - μB g J wheree

B me

2h

=microis the Bohr magneton μ B asymp 92732times10-24 JouleTesla and g is the gyromagnetic ratio

WB = - μ B

Therefore after applying of an external magnetic field the energy level |γ J Mgtsplits into 2J+1 components which refer to the quantum numbers

M = J J-1 hellip -J

In case of the LS-coupling )1(2)1()1()1(1

++++minus+

+=JJ

SSLLJJg

In case of a pure orbital angular momentum (J=L S=0) g = 1

In case of a pure spin angular momentum (J=S L=0) g = 2

Fluorescence polarization due to the Zeeman effect

M = ndash1Jrsquorsquo = 1

Jrsquo = 0

M = 0

M = 1M = 0

e perp Ze perp Z

e ZΔM=0

ΔM=plusmn1

σndash - component

π - component

σ+ - component

Z Н e

Observation the fluorescence from the excited state Jrsquo=1 to the ground state Jrsquorsquo=0 along the magnetic field shows a spectral line consisting of two components (σ+ and σ-) Observation along the direction perpendicular to the magnetic field shows a spectral lineconsisting of three components (σ+ σ- and π)

Radiation transitions

According to the Quantum Electrodynamics the probabilityof radiation transition can be presented in the form

Expanding the exponent over the powers of kr one can obtain particular expressions for multipole radiation The first term of the expansion (itrsquos 1) eikr = 1 + ikr + describes the electric dipole emission and absorption

dOnMJeJMmc

edW

dOnMJeJMmc

edW

ki

kab

ki

kem

ρρ

ρρ

γγπ

ω

γγπ

ω

2

23

2

2

23

2

2

)1(2

primeprimeprime=

+primeprimeprime=

minus kr

kr

pe

pe

h

h

Quantization of the electromagnetic field

( )21nk += ρωhfieldW

( )sum +minus=

primeprimeprimesdot=


iii

kind

DM

ksp

DM

mce

dOIMJJMc

dW

dOMJJMc

dW

slM

M

M

22

42

2

2

2

2

3

3

h

r

h

r

h

ωρ

ρ

γmicroγπ

γmicroγπω

Multipole emission and absorption

Magnetic dipole emission and absorption

Electric dipole emission and absorption

sum=



ii

kind

DE

ksp

DE

e

dOIMJJMc

dW

dOMJJMc

dW

rD

De

De

ωρ

ρ

γγπ

γγπω

2

2

2

2

3

3

42

h

h

Selection rules

ΔJ = 0 plusmn1ΔMJ = 0 plusmn1ΔP = 0 (+ harr + or

minus harr minus )

Selection rules

ΔJ = 0 plusmn1ΔMJ = 0 plusmn1ΔP ne 0 (+ harr minus)

A link between theoretical and experimental quantitiesProvided only emission but no other processes like collisions with other particles orinternal conversions occur a measurement of the fluorescence lifetime τ directlyyields the transition probability Amn which gives you also Bmn

Amn= 1 τ

From theory the quantity Rmn is calculated which is linked to Amn

Here follows the relation ships between the integrated absorption cross section σo the Einstein coefficient Bmn the quantity Rmn and the oscillator strength f

What is Spectroscopy

The study of molecularstructure and dynamics throughthe absorption emission and

scattering of light

URL Internet Skript



List of References












Visible Light

Spectral Areas

700 600 500 400

Wavelength nm

ν = сλ (Hz)


Type of Radiation












Light Polarization

E


Unpolarized light

E


Linear Polarization







=

1

2arctannn

Bθ

n1

n2p-polarization



s-polarization





dN2dt = B12

u(ν) N1dN







Albert Einstein





T = 10-εcl



AA NN




I = I0(1 - σ N l)



chBd 0








and ∆νL = γ

τh

asymp∆E

( )2

20 2

21)(

+minus

=γ

γ

πν

vvI




sim 107 sim 10-4


sim10-4 sim 10-15



sim 109 sim 10-2



sim 1012 sim 101


plusmn=

cZ

0v1νν


minus=

Tkm

kTmf

2vexp

2)v(

2Z

Z π


( )

∆minus

minus∆

= 2

202ln4exp12ln4)(

DD

Iννν

νπν where

mTk

cD2ln22 0ν

ν =∆




P12 = P1 + P2


Wavelength λ = hmv


Nobelpreis 1929







φ = φ1+φ2I = |φ1+φ2|2


















5 Dez 1901+ 1 Feb 1976

Hydrogen Atom

reZ

mH e

e 0

22

2


h

2

2

2

2

2

22

zyxe partpart

+partpart

+partpart

=nabla ( )φθ 1 222

2 Λ+

partpart

partpart

=nablar

rrre

( )θ

θθθθθ

φθpartpart

partpart

+partpart

=Λ sinsin

1sin

1 2

2

22

Hamiltonian

Wavefunctions

-

+




Polar coordinates

kkk EH ψψ =


230

10

02aeR

ar

minus

=

230

2

020 22

2 0

a

ear

R

ar

minus

minus

= 230

2

021 62

0

a

ear

R

ar

minus

=




s 0 0 1(4 π)frac12 14 π

p11

plusmn10




d222

plusmn2plusmn10





f

3333




(716 π)frac12 (5 cos3 θ - 3 cos θ)



g

44444















1

2

2




11

s = 1(4p)frac1200

Wave Functions|ml|l



l = 0 m = 0

l = 2






Nobelpreis 1965


K32124

12

0

2

0

=minus= nna

eEnl πε







j = l + s

l s

j = l ndash frac12

j = l + frac12

2

4

3

42

21

)1( h

mellnZE jj +




z-projection


z-projection


TJ

me

eB

24102792

minussdot==h

micro

sBsZ

Bs

lBlZ

Bl

msm

l


micromicro

22minus=

minus=minus=

minus=

rr

rr









Nobelpreis 1945





JS L12 +

oJ

S L12 +

- even states

- odd states

J + J ge 1

S = 1 Triplet state

L = 0 S -state

L = 2 D -state

S = 0 Singlet state

L = 1 P -state


ΔM = 0 plusmn1

M = ndash1

J = 1

J = 0

M = 0

M = 1M = 0

Z

e perp Ze perp Z

e Z

e

ΔM = ndash 1

ΔM=0

ΔM=plusmn1

ΔM = 1



L S

Jmin = |L ndash S|

Jmax = L + SJ+1J

L S

Jmin = |L ndash S|

Jmax = L + SJ+1J

VSO = A LS



А gt 0

А gt 0



J I

Fmin = |J ndash I|

Fmax = J + IF+1F

J I

Fmin = |J ndash I|

Fmax = J + IF+1F

Vhpf = AI JI


Lande interval rule






sum partpartpart

+minus=+=βα βα

αβmicroϕ

micro

2

6)0(

xxQeHWWW Q

F = J + I


H0 ψn(0) = E(0) ψn









sum=n

nn qcq )()( )0(ψψ




kmEE

kVmmVkE

m mkk ne

minus= sum )2(





H0 ψn(0) = E(0) ψn

(0) (H0 + V) ψ = E ψwhere E(0)

n = E(0)n


sum Ψ=Ψn

nn qcq )()( )0()0()0(


(0)(q)





n

( )sumprime

prime =minusn







0

21

22221

11211

=

minus

minusminus

EVVV

VEVVVVEV

NNNN

N

N

L

LLLL

L

L






J JJ

ZZZMJ EE

MJDMJMJDMJMJDMJE

γ γγγ

γγγγγγ 2EE



22


∆

plusmn=∆ γγ2E



M = ndash1

Jrsquo = 1

Jrsquorsquo = 0

M = 0

M = 1

M = 0

e perp Ze perp Z

e Z

ΔM=0

ΔM=plusmn1

σ - component

π - component

σ - component

Z E e





B me

2h


WB = - μ B


M = J J-1 hellip -J


++++minus+

+=JJ

SSLLJJg





Jrsquo = 0

M = 0

M = 1M = 0

e perp Ze perp Z

e ZΔM=0

ΔM=plusmn1

σndash - component

π - component

σ+ - component

Z Н e





dOnMJeJMmc

edW

dOnMJeJMmc

edW

ki

kab

ki

kem

ρρ

ρρ

γγπ

ω

γγπ

ω

2

23

2

2

23

2

2

)1(2

primeprimeprime=

+primeprimeprime=

minus kr

kr

pe

pe

h

h



( )sum +minus=



iii

kind

DM

ksp

DM

mce

dOIMJJMc

dW

dOMJJMc

dW

slM

M

M

22

42

2

2

2

2

3

3

h

r

h

r

h

ωρ

ρ

γmicroγπ

γmicroγπω




sum=



ii

kind

DE

ksp

DE

e

dOIMJJMc

dW

dOMJJMc

dW

rD

De

De

ωρ

ρ

γγπ

γγπω

2

2

2

2

3

3

42

h

h

Selection rules


minus harr minus )

Selection rules



Amn= 1 τ



URL Internet Skript



List of References












Visible Light

Spectral Areas

700 600 500 400

Wavelength nm

ν = сλ (Hz)


Type of Radiation












Light Polarization

E


Unpolarized light

E


Linear Polarization







=

1

2arctannn

Bθ

n1

n2p-polarization



s-polarization





dN2dt = B12

u(ν) N1dN







Albert Einstein





T = 10-εcl



AA NN




I = I0(1 - σ N l)



chBd 0








and ∆νL = γ

τh

asymp∆E

( )2

20 2

21)(

+minus

=γ

γ

πν

vvI




sim 107 sim 10-4


sim10-4 sim 10-15



sim 109 sim 10-2



sim 1012 sim 101


plusmn=

cZ

0v1νν


minus=

Tkm

kTmf

2vexp

2)v(

2Z

Z π


( )

∆minus

minus∆

= 2

202ln4exp12ln4)(

DD

Iννν

νπν where

mTk

cD2ln22 0ν

ν =∆




P12 = P1 + P2


Wavelength λ = hmv


Nobelpreis 1929







φ = φ1+φ2I = |φ1+φ2|2


















5 Dez 1901+ 1 Feb 1976

Hydrogen Atom

reZ

mH e

e 0

22

2


h

2

2

2

2

2

22

zyxe partpart

+partpart

+partpart

=nabla ( )φθ 1 222

2 Λ+

partpart

partpart

=nablar

rrre

( )θ

θθθθθ

φθpartpart

partpart

+partpart

=Λ sinsin

1sin

1 2

2

22

Hamiltonian

Wavefunctions

-

+




Polar coordinates

kkk EH ψψ =


230

10

02aeR

ar

minus

=

230

2

020 22

2 0

a

ear

R

ar

minus

minus

= 230

2

021 62

0

a

ear

R

ar

minus

=




s 0 0 1(4 π)frac12 14 π

p11

plusmn10




d222

plusmn2plusmn10





f

3333




(716 π)frac12 (5 cos3 θ - 3 cos θ)



g

44444















1

2

2




11

s = 1(4p)frac1200

Wave Functions|ml|l



l = 0 m = 0

l = 2






Nobelpreis 1965


K32124

12

0

2

0

=minus= nna

eEnl πε







j = l + s

l s

j = l ndash frac12

j = l + frac12

2

4

3

42

21

)1( h

mellnZE jj +




z-projection


z-projection


TJ

me

eB

24102792

minussdot==h

micro

sBsZ

Bs

lBlZ

Bl

msm

l


micromicro

22minus=

minus=minus=

minus=

rr

rr









Nobelpreis 1945





JS L12 +

oJ

S L12 +

- even states

- odd states

J + J ge 1

S = 1 Triplet state

L = 0 S -state

L = 2 D -state

S = 0 Singlet state

L = 1 P -state


ΔM = 0 plusmn1

M = ndash1

J = 1

J = 0

M = 0

M = 1M = 0

Z

e perp Ze perp Z

e Z

e

ΔM = ndash 1

ΔM=0

ΔM=plusmn1

ΔM = 1



L S

Jmin = |L ndash S|

Jmax = L + SJ+1J

L S

Jmin = |L ndash S|

Jmax = L + SJ+1J

VSO = A LS



А gt 0

А gt 0



J I

Fmin = |J ndash I|

Fmax = J + IF+1F

J I

Fmin = |J ndash I|

Fmax = J + IF+1F

Vhpf = AI JI


Lande interval rule






sum partpartpart

+minus=+=βα βα

αβmicroϕ

micro

2

6)0(

xxQeHWWW Q

F = J + I


H0 ψn(0) = E(0) ψn









sum=n

nn qcq )()( )0(ψψ




kmEE

kVmmVkE

m mkk ne

minus= sum )2(





H0 ψn(0) = E(0) ψn

(0) (H0 + V) ψ = E ψwhere E(0)

n = E(0)n


sum Ψ=Ψn

nn qcq )()( )0()0()0(


(0)(q)





n

( )sumprime

prime =minusn







0

21

22221

11211

=

minus

minusminus

EVVV

VEVVVVEV

NNNN

N

N

L

LLLL

L

L






J JJ

ZZZMJ EE

MJDMJMJDMJMJDMJE

γ γγγ

γγγγγγ 2EE



22


∆

plusmn=∆ γγ2E



M = ndash1

Jrsquo = 1

Jrsquorsquo = 0

M = 0

M = 1

M = 0

e perp Ze perp Z

e Z

ΔM=0

ΔM=plusmn1

σ - component

π - component

σ - component

Z E e





B me

2h


WB = - μ B


M = J J-1 hellip -J


++++minus+

+=JJ

SSLLJJg





Jrsquo = 0

M = 0

M = 1M = 0

e perp Ze perp Z

e ZΔM=0

ΔM=plusmn1

σndash - component

π - component

σ+ - component

Z Н e





dOnMJeJMmc

edW

dOnMJeJMmc

edW

ki

kab

ki

kem

ρρ

ρρ

γγπ

ω

γγπ

ω

2

23

2

2

23

2

2

)1(2

primeprimeprime=

+primeprimeprime=

minus kr

kr

pe

pe

h

h



( )sum +minus=



iii

kind

DM

ksp

DM

mce

dOIMJJMc

dW

dOMJJMc

dW

slM

M

M

22

42

2

2

2

2

3

3

h

r

h

r

h

ωρ

ρ

γmicroγπ

γmicroγπω




sum=



ii

kind

DE

ksp

DE

e

dOIMJJMc

dW

dOMJJMc

dW

rD

De

De

ωρ

ρ

γγπ

γγπω

2

2

2

2

3

3

42

h

h

Selection rules


minus harr minus )

Selection rules



Amn= 1 τ



List of References












Visible Light

Spectral Areas

700 600 500 400

Wavelength nm

ν = сλ (Hz)


Type of Radiation












Light Polarization

E


Unpolarized light

E


Linear Polarization







=

1

2arctannn

Bθ

n1

n2p-polarization



s-polarization





dN2dt = B12

u(ν) N1dN







Albert Einstein





T = 10-εcl



AA NN




I = I0(1 - σ N l)



chBd 0








and ∆νL = γ

τh

asymp∆E

( )2

20 2

21)(

+minus

=γ

γ

πν

vvI




sim 107 sim 10-4


sim10-4 sim 10-15



sim 109 sim 10-2



sim 1012 sim 101


plusmn=

cZ

0v1νν


minus=

Tkm

kTmf

2vexp

2)v(

2Z

Z π


( )

∆minus

minus∆

= 2

202ln4exp12ln4)(

DD

Iννν

νπν where

mTk

cD2ln22 0ν

ν =∆




P12 = P1 + P2


Wavelength λ = hmv


Nobelpreis 1929







φ = φ1+φ2I = |φ1+φ2|2


















5 Dez 1901+ 1 Feb 1976

Hydrogen Atom

reZ

mH e

e 0

22

2


h

2

2

2

2

2

22

zyxe partpart

+partpart

+partpart

=nabla ( )φθ 1 222

2 Λ+

partpart

partpart

=nablar

rrre

( )θ

θθθθθ

φθpartpart

partpart

+partpart

=Λ sinsin

1sin

1 2

2

22

Hamiltonian

Wavefunctions

-

+




Polar coordinates

kkk EH ψψ =


230

10

02aeR

ar

minus

=

230

2

020 22

2 0

a

ear

R

ar

minus

minus

= 230

2

021 62

0

a

ear

R

ar

minus

=




s 0 0 1(4 π)frac12 14 π

p11

plusmn10




d222

plusmn2plusmn10





f

3333




(716 π)frac12 (5 cos3 θ - 3 cos θ)



g

44444















1

2

2




11

s = 1(4p)frac1200

Wave Functions|ml|l



l = 0 m = 0

l = 2






Nobelpreis 1965


K32124

12

0

2

0

=minus= nna

eEnl πε







j = l + s

l s

j = l ndash frac12

j = l + frac12

2

4

3

42

21

)1( h

mellnZE jj +




z-projection


z-projection


TJ

me

eB

24102792

minussdot==h

micro

sBsZ

Bs

lBlZ

Bl

msm

l


micromicro

22minus=

minus=minus=

minus=

rr

rr









Nobelpreis 1945





JS L12 +

oJ

S L12 +

- even states

- odd states

J + J ge 1

S = 1 Triplet state

L = 0 S -state

L = 2 D -state

S = 0 Singlet state

L = 1 P -state


ΔM = 0 plusmn1

M = ndash1

J = 1

J = 0

M = 0

M = 1M = 0

Z

e perp Ze perp Z

e Z

e

ΔM = ndash 1

ΔM=0

ΔM=plusmn1

ΔM = 1



L S

Jmin = |L ndash S|

Jmax = L + SJ+1J

L S

Jmin = |L ndash S|

Jmax = L + SJ+1J

VSO = A LS



А gt 0

А gt 0



J I

Fmin = |J ndash I|

Fmax = J + IF+1F

J I

Fmin = |J ndash I|

Fmax = J + IF+1F

Vhpf = AI JI


Lande interval rule






sum partpartpart

+minus=+=βα βα

αβmicroϕ

micro

2

6)0(

xxQeHWWW Q

F = J + I


H0 ψn(0) = E(0) ψn









sum=n

nn qcq )()( )0(ψψ




kmEE

kVmmVkE

m mkk ne

minus= sum )2(





H0 ψn(0) = E(0) ψn

(0) (H0 + V) ψ = E ψwhere E(0)

n = E(0)n


sum Ψ=Ψn

nn qcq )()( )0()0()0(


(0)(q)





n

( )sumprime

prime =minusn







0

21

22221

11211

=

minus

minusminus

EVVV

VEVVVVEV

NNNN

N

N

L

LLLL

L

L






J JJ

ZZZMJ EE

MJDMJMJDMJMJDMJE

γ γγγ

γγγγγγ 2EE



22


∆

plusmn=∆ γγ2E



M = ndash1

Jrsquo = 1

Jrsquorsquo = 0

M = 0

M = 1

M = 0

e perp Ze perp Z

e Z

ΔM=0

ΔM=plusmn1

σ - component

π - component

σ - component

Z E e





B me

2h


WB = - μ B


M = J J-1 hellip -J


++++minus+

+=JJ

SSLLJJg





Jrsquo = 0

M = 0

M = 1M = 0

e perp Ze perp Z

e ZΔM=0

ΔM=plusmn1

σndash - component

π - component

σ+ - component

Z Н e





dOnMJeJMmc

edW

dOnMJeJMmc

edW

ki

kab

ki

kem

ρρ

ρρ

γγπ

ω

γγπ

ω

2

23

2

2

23

2

2

)1(2

primeprimeprime=

+primeprimeprime=

minus kr

kr

pe

pe

h

h



( )sum +minus=



iii

kind

DM

ksp

DM

mce

dOIMJJMc

dW

dOMJJMc

dW

slM

M

M

22

42

2

2

2

2

3

3

h

r

h

r

h

ωρ

ρ

γmicroγπ

γmicroγπω




sum=



ii

kind

DE

ksp

DE

e

dOIMJJMc

dW

dOMJJMc

dW

rD

De

De

ωρ

ρ

γγπ

γγπω

2

2

2

2

3

3

42

h

h

Selection rules


minus harr minus )

Selection rules



Amn= 1 τ




Visible Light

Spectral Areas

700 600 500 400

Wavelength nm

ν = сλ (Hz)


Type of Radiation












Light Polarization

E


Unpolarized light

E


Linear Polarization







=

1

2arctannn

Bθ

n1

n2p-polarization



s-polarization





dN2dt = B12

u(ν) N1dN







Albert Einstein





T = 10-εcl



AA NN




I = I0(1 - σ N l)



chBd 0








and ∆νL = γ

τh

asymp∆E

( )2

20 2

21)(

+minus

=γ

γ

πν

vvI




sim 107 sim 10-4


sim10-4 sim 10-15



sim 109 sim 10-2



sim 1012 sim 101


plusmn=

cZ

0v1νν


minus=

Tkm

kTmf

2vexp

2)v(

2Z

Z π


( )

∆minus

minus∆

= 2

202ln4exp12ln4)(

DD

Iννν

νπν where

mTk

cD2ln22 0ν

ν =∆




P12 = P1 + P2


Wavelength λ = hmv


Nobelpreis 1929







φ = φ1+φ2I = |φ1+φ2|2


















5 Dez 1901+ 1 Feb 1976

Hydrogen Atom

reZ

mH e

e 0

22

2


h

2

2

2

2

2

22

zyxe partpart

+partpart

+partpart

=nabla ( )φθ 1 222

2 Λ+

partpart

partpart

=nablar

rrre

( )θ

θθθθθ

φθpartpart

partpart

+partpart

=Λ sinsin

1sin

1 2

2

22

Hamiltonian

Wavefunctions

-

+




Polar coordinates

kkk EH ψψ =


230

10

02aeR

ar

minus

=

230

2

020 22

2 0

a

ear

R

ar

minus

minus

= 230

2

021 62

0

a

ear

R

ar

minus

=




s 0 0 1(4 π)frac12 14 π

p11

plusmn10




d222

plusmn2plusmn10





f

3333




(716 π)frac12 (5 cos3 θ - 3 cos θ)



g

44444















1

2

2




11

s = 1(4p)frac1200

Wave Functions|ml|l



l = 0 m = 0

l = 2






Nobelpreis 1965


K32124

12

0

2

0

=minus= nna

eEnl πε







j = l + s

l s

j = l ndash frac12

j = l + frac12

2

4

3

42

21

)1( h

mellnZE jj +




z-projection


z-projection


TJ

me

eB

24102792

minussdot==h

micro

sBsZ

Bs

lBlZ

Bl

msm

l


micromicro

22minus=

minus=minus=

minus=

rr

rr









Nobelpreis 1945





JS L12 +

oJ

S L12 +

- even states

- odd states

J + J ge 1

S = 1 Triplet state

L = 0 S -state

L = 2 D -state

S = 0 Singlet state

L = 1 P -state


ΔM = 0 plusmn1

M = ndash1

J = 1

J = 0

M = 0

M = 1M = 0

Z

e perp Ze perp Z

e Z

e

ΔM = ndash 1

ΔM=0

ΔM=plusmn1

ΔM = 1



L S

Jmin = |L ndash S|

Jmax = L + SJ+1J

L S

Jmin = |L ndash S|

Jmax = L + SJ+1J

VSO = A LS



А gt 0

А gt 0



J I

Fmin = |J ndash I|

Fmax = J + IF+1F

J I

Fmin = |J ndash I|

Fmax = J + IF+1F

Vhpf = AI JI


Lande interval rule






sum partpartpart

+minus=+=βα βα

αβmicroϕ

micro

2

6)0(

xxQeHWWW Q

F = J + I


H0 ψn(0) = E(0) ψn









sum=n

nn qcq )()( )0(ψψ




kmEE

kVmmVkE

m mkk ne

minus= sum )2(





H0 ψn(0) = E(0) ψn

(0) (H0 + V) ψ = E ψwhere E(0)

n = E(0)n


sum Ψ=Ψn

nn qcq )()( )0()0()0(


(0)(q)





n

( )sumprime

prime =minusn







0

21

22221

11211

=

minus

minusminus

EVVV

VEVVVVEV

NNNN

N

N

L

LLLL

L

L






J JJ

ZZZMJ EE

MJDMJMJDMJMJDMJE

γ γγγ

γγγγγγ 2EE



22


∆

plusmn=∆ γγ2E



M = ndash1

Jrsquo = 1

Jrsquorsquo = 0

M = 0

M = 1

M = 0

e perp Ze perp Z

e Z

ΔM=0

ΔM=plusmn1

σ - component

π - component

σ - component

Z E e





B me

2h


WB = - μ B


M = J J-1 hellip -J


++++minus+

+=JJ

SSLLJJg





Jrsquo = 0

M = 0

M = 1M = 0

e perp Ze perp Z

e ZΔM=0

ΔM=plusmn1

σndash - component

π - component

σ+ - component

Z Н e





dOnMJeJMmc

edW

dOnMJeJMmc

edW

ki

kab

ki

kem

ρρ

ρρ

γγπ

ω

γγπ

ω

2

23

2

2

23

2

2

)1(2

primeprimeprime=

+primeprimeprime=

minus kr

kr

pe

pe

h

h



( )sum +minus=



iii

kind

DM

ksp

DM

mce

dOIMJJMc

dW

dOMJJMc

dW

slM

M

M

22

42

2

2

2

2

3

3

h

r

h

r

h

ωρ

ρ

γmicroγπ

γmicroγπω




sum=



ii

kind

DE

ksp

DE

e

dOIMJJMc

dW

dOMJJMc

dW

rD

De

De

ωρ

ρ

γγπ

γγπω

2

2

2

2

3

3

42

h

h

Selection rules


minus harr minus )

Selection rules



Amn= 1 τ




Type of Radiation












Light Polarization

E


Unpolarized light

E


Linear Polarization







=

1

2arctannn

Bθ

n1

n2p-polarization



s-polarization





dN2dt = B12

u(ν) N1dN







Albert Einstein





T = 10-εcl



AA NN




I = I0(1 - σ N l)



chBd 0








and ∆νL = γ

τh

asymp∆E

( )2

20 2

21)(

+minus

=γ

γ

πν

vvI




sim 107 sim 10-4


sim10-4 sim 10-15



sim 109 sim 10-2



sim 1012 sim 101


plusmn=

cZ

0v1νν


minus=

Tkm

kTmf

2vexp

2)v(

2Z

Z π


( )

∆minus

minus∆

= 2

202ln4exp12ln4)(

DD

Iννν

νπν where

mTk

cD2ln22 0ν

ν =∆




P12 = P1 + P2


Wavelength λ = hmv


Nobelpreis 1929







φ = φ1+φ2I = |φ1+φ2|2


















5 Dez 1901+ 1 Feb 1976

Hydrogen Atom

reZ

mH e

e 0

22

2


h

2

2

2

2

2

22

zyxe partpart

+partpart

+partpart

=nabla ( )φθ 1 222

2 Λ+

partpart

partpart

=nablar

rrre

( )θ

θθθθθ

φθpartpart

partpart

+partpart

=Λ sinsin

1sin

1 2

2

22

Hamiltonian

Wavefunctions

-

+




Polar coordinates

kkk EH ψψ =


230

10

02aeR

ar

minus

=

230

2

020 22

2 0

a

ear

R

ar

minus

minus

= 230

2

021 62

0

a

ear

R

ar

minus

=




s 0 0 1(4 π)frac12 14 π

p11

plusmn10




d222

plusmn2plusmn10





f

3333




(716 π)frac12 (5 cos3 θ - 3 cos θ)



g

44444















1

2

2




11

s = 1(4p)frac1200

Wave Functions|ml|l



l = 0 m = 0

l = 2






Nobelpreis 1965


K32124

12

0

2

0

=minus= nna

eEnl πε







j = l + s

l s

j = l ndash frac12

j = l + frac12

2

4

3

42

21

)1( h

mellnZE jj +




z-projection


z-projection


TJ

me

eB

24102792

minussdot==h

micro

sBsZ

Bs

lBlZ

Bl

msm

l


micromicro

22minus=

minus=minus=

minus=

rr

rr









Nobelpreis 1945





JS L12 +

oJ

S L12 +

- even states

- odd states

J + J ge 1

S = 1 Triplet state

L = 0 S -state

L = 2 D -state

S = 0 Singlet state

L = 1 P -state


ΔM = 0 plusmn1

M = ndash1

J = 1

J = 0

M = 0

M = 1M = 0

Z

e perp Ze perp Z

e Z

e

ΔM = ndash 1

ΔM=0

ΔM=plusmn1

ΔM = 1



L S

Jmin = |L ndash S|

Jmax = L + SJ+1J

L S

Jmin = |L ndash S|

Jmax = L + SJ+1J

VSO = A LS



А gt 0

А gt 0



J I

Fmin = |J ndash I|

Fmax = J + IF+1F

J I

Fmin = |J ndash I|

Fmax = J + IF+1F

Vhpf = AI JI


Lande interval rule






sum partpartpart

+minus=+=βα βα

αβmicroϕ

micro

2

6)0(

xxQeHWWW Q

F = J + I


H0 ψn(0) = E(0) ψn









sum=n

nn qcq )()( )0(ψψ




kmEE

kVmmVkE

m mkk ne

minus= sum )2(





H0 ψn(0) = E(0) ψn

(0) (H0 + V) ψ = E ψwhere E(0)

n = E(0)n


sum Ψ=Ψn

nn qcq )()( )0()0()0(


(0)(q)





n

( )sumprime

prime =minusn







0

21

22221

11211

=

minus

minusminus

EVVV

VEVVVVEV

NNNN

N

N

L

LLLL

L

L






J JJ

ZZZMJ EE

MJDMJMJDMJMJDMJE

γ γγγ

γγγγγγ 2EE



22


∆

plusmn=∆ γγ2E



M = ndash1

Jrsquo = 1

Jrsquorsquo = 0

M = 0

M = 1

M = 0

e perp Ze perp Z

e Z

ΔM=0

ΔM=plusmn1

σ - component

π - component

σ - component

Z E e





B me

2h


WB = - μ B


M = J J-1 hellip -J


++++minus+

+=JJ

SSLLJJg





Jrsquo = 0

M = 0

M = 1M = 0

e perp Ze perp Z

e ZΔM=0

ΔM=plusmn1

σndash - component

π - component

σ+ - component

Z Н e





dOnMJeJMmc

edW

dOnMJeJMmc

edW

ki

kab

ki

kem

ρρ

ρρ

γγπ

ω

γγπ

ω

2

23

2

2

23

2

2

)1(2

primeprimeprime=

+primeprimeprime=

minus kr

kr

pe

pe

h

h



( )sum +minus=



iii

kind

DM

ksp

DM

mce

dOIMJJMc

dW

dOMJJMc

dW

slM

M

M

22

42

2

2

2

2

3

3

h

r

h

r

h

ωρ

ρ

γmicroγπ

γmicroγπω




sum=



ii

kind

DE

ksp

DE

e

dOIMJJMc

dW

dOMJJMc

dW

rD

De

De

ωρ

ρ

γγπ

γγπω

2

2

2

2

3

3

42

h

h

Selection rules


minus harr minus )

Selection rules



Amn= 1 τ




Light Polarization

E


Unpolarized light

E


Linear Polarization







=

1

2arctannn

Bθ

n1

n2p-polarization



s-polarization





dN2dt = B12

u(ν) N1dN







Albert Einstein





T = 10-εcl



AA NN




I = I0(1 - σ N l)



chBd 0








and ∆νL = γ

τh

asymp∆E

( )2

20 2

21)(

+minus

=γ

γ

πν

vvI




sim 107 sim 10-4


sim10-4 sim 10-15



sim 109 sim 10-2



sim 1012 sim 101


plusmn=

cZ

0v1νν


minus=

Tkm

kTmf

2vexp

2)v(

2Z

Z π


( )

∆minus

minus∆

= 2

202ln4exp12ln4)(

DD

Iννν

νπν where

mTk

cD2ln22 0ν

ν =∆




P12 = P1 + P2


Wavelength λ = hmv


Nobelpreis 1929







φ = φ1+φ2I = |φ1+φ2|2


















5 Dez 1901+ 1 Feb 1976

Hydrogen Atom

reZ

mH e

e 0

22

2


h

2

2

2

2

2

22

zyxe partpart

+partpart

+partpart

=nabla ( )φθ 1 222

2 Λ+

partpart

partpart

=nablar

rrre

( )θ

θθθθθ

φθpartpart

partpart

+partpart

=Λ sinsin

1sin

1 2

2

22

Hamiltonian

Wavefunctions

-

+




Polar coordinates

kkk EH ψψ =


230

10

02aeR

ar

minus

=

230

2

020 22

2 0

a

ear

R

ar

minus

minus

= 230

2

021 62

0

a

ear

R

ar

minus

=




s 0 0 1(4 π)frac12 14 π

p11

plusmn10




d222

plusmn2plusmn10





f

3333




(716 π)frac12 (5 cos3 θ - 3 cos θ)



g

44444















1

2

2




11

s = 1(4p)frac1200

Wave Functions|ml|l



l = 0 m = 0

l = 2






Nobelpreis 1965


K32124

12

0

2

0

=minus= nna

eEnl πε







j = l + s

l s

j = l ndash frac12

j = l + frac12

2

4

3

42

21

)1( h

mellnZE jj +




z-projection


z-projection


TJ

me

eB

24102792

minussdot==h

micro

sBsZ

Bs

lBlZ

Bl

msm

l


micromicro

22minus=

minus=minus=

minus=

rr

rr









Nobelpreis 1945





JS L12 +

oJ

S L12 +

- even states

- odd states

J + J ge 1

S = 1 Triplet state

L = 0 S -state

L = 2 D -state

S = 0 Singlet state

L = 1 P -state


ΔM = 0 plusmn1

M = ndash1

J = 1

J = 0

M = 0

M = 1M = 0

Z

e perp Ze perp Z

e Z

e

ΔM = ndash 1

ΔM=0

ΔM=plusmn1

ΔM = 1



L S

Jmin = |L ndash S|

Jmax = L + SJ+1J

L S

Jmin = |L ndash S|

Jmax = L + SJ+1J

VSO = A LS



А gt 0

А gt 0



J I

Fmin = |J ndash I|

Fmax = J + IF+1F

J I

Fmin = |J ndash I|

Fmax = J + IF+1F

Vhpf = AI JI


Lande interval rule






sum partpartpart

+minus=+=βα βα

αβmicroϕ

micro

2

6)0(

xxQeHWWW Q

F = J + I


H0 ψn(0) = E(0) ψn









sum=n

nn qcq )()( )0(ψψ




kmEE

kVmmVkE

m mkk ne

minus= sum )2(





H0 ψn(0) = E(0) ψn

(0) (H0 + V) ψ = E ψwhere E(0)

n = E(0)n


sum Ψ=Ψn

nn qcq )()( )0()0()0(


(0)(q)





n

( )sumprime

prime =minusn







0

21

22221

11211

=

minus

minusminus

EVVV

VEVVVVEV

NNNN

N

N

L

LLLL

L

L






J JJ

ZZZMJ EE

MJDMJMJDMJMJDMJE

γ γγγ

γγγγγγ 2EE



22


∆

plusmn=∆ γγ2E



M = ndash1

Jrsquo = 1

Jrsquorsquo = 0

M = 0

M = 1

M = 0

e perp Ze perp Z

e Z

ΔM=0

ΔM=plusmn1

σ - component

π - component

σ - component

Z E e





B me

2h


WB = - μ B


M = J J-1 hellip -J


++++minus+

+=JJ

SSLLJJg





Jrsquo = 0

M = 0

M = 1M = 0

e perp Ze perp Z

e ZΔM=0

ΔM=plusmn1

σndash - component

π - component

σ+ - component

Z Н e





dOnMJeJMmc

edW

dOnMJeJMmc

edW

ki

kab

ki

kem

ρρ

ρρ

γγπ

ω

γγπ

ω

2

23

2

2

23

2

2

)1(2

primeprimeprime=

+primeprimeprime=

minus kr

kr

pe

pe

h

h



( )sum +minus=



iii

kind

DM

ksp

DM

mce

dOIMJJMc

dW

dOMJJMc

dW

slM

M

M

22

42

2

2

2

2

3

3

h

r

h

r

h

ωρ

ρ

γmicroγπ

γmicroγπω




sum=



ii

kind

DE

ksp

DE

e

dOIMJJMc

dW

dOMJJMc

dW

rD

De

De

ωρ

ρ

γγπ

γγπω

2

2

2

2

3

3

42

h

h

Selection rules


minus harr minus )

Selection rules



Amn= 1 τ



Linear Polarization







=

1

2arctannn

Bθ

n1

n2p-polarization



s-polarization





dN2dt = B12

u(ν) N1dN







Albert Einstein





T = 10-εcl



AA NN




I = I0(1 - σ N l)



chBd 0








and ∆νL = γ

τh

asymp∆E

( )2

20 2

21)(

+minus

=γ

γ

πν

vvI




sim 107 sim 10-4


sim10-4 sim 10-15



sim 109 sim 10-2



sim 1012 sim 101


plusmn=

cZ

0v1νν


minus=

Tkm

kTmf

2vexp

2)v(

2Z

Z π


( )

∆minus

minus∆

= 2

202ln4exp12ln4)(

DD

Iννν

νπν where

mTk

cD2ln22 0ν

ν =∆




P12 = P1 + P2


Wavelength λ = hmv


Nobelpreis 1929







φ = φ1+φ2I = |φ1+φ2|2


















5 Dez 1901+ 1 Feb 1976

Hydrogen Atom

reZ

mH e

e 0

22

2


h

2

2

2

2

2

22

zyxe partpart

+partpart

+partpart

=nabla ( )φθ 1 222

2 Λ+

partpart

partpart

=nablar

rrre

( )θ

θθθθθ

φθpartpart

partpart

+partpart

=Λ sinsin

1sin

1 2

2

22

Hamiltonian

Wavefunctions

-

+




Polar coordinates

kkk EH ψψ =


230

10

02aeR

ar

minus

=

230

2

020 22

2 0

a

ear

R

ar

minus

minus

= 230

2

021 62

0

a

ear

R

ar

minus

=




s 0 0 1(4 π)frac12 14 π

p11

plusmn10




d222

plusmn2plusmn10





f

3333




(716 π)frac12 (5 cos3 θ - 3 cos θ)



g

44444















1

2

2




11

s = 1(4p)frac1200

Wave Functions|ml|l



l = 0 m = 0

l = 2






Nobelpreis 1965


K32124

12

0

2

0

=minus= nna

eEnl πε







j = l + s

l s

j = l ndash frac12

j = l + frac12

2

4

3

42

21

)1( h

mellnZE jj +




z-projection


z-projection


TJ

me

eB

24102792

minussdot==h

micro

sBsZ

Bs

lBlZ

Bl

msm

l


micromicro

22minus=

minus=minus=

minus=

rr

rr









Nobelpreis 1945





JS L12 +

oJ

S L12 +

- even states

- odd states

J + J ge 1

S = 1 Triplet state

L = 0 S -state

L = 2 D -state

S = 0 Singlet state

L = 1 P -state


ΔM = 0 plusmn1

M = ndash1

J = 1

J = 0

M = 0

M = 1M = 0

Z

e perp Ze perp Z

e Z

e

ΔM = ndash 1

ΔM=0

ΔM=plusmn1

ΔM = 1



L S

Jmin = |L ndash S|

Jmax = L + SJ+1J

L S

Jmin = |L ndash S|

Jmax = L + SJ+1J

VSO = A LS



А gt 0

А gt 0



J I

Fmin = |J ndash I|

Fmax = J + IF+1F

J I

Fmin = |J ndash I|

Fmax = J + IF+1F

Vhpf = AI JI


Lande interval rule






sum partpartpart

+minus=+=βα βα

αβmicroϕ

micro

2

6)0(

xxQeHWWW Q

F = J + I


H0 ψn(0) = E(0) ψn









sum=n

nn qcq )()( )0(ψψ




kmEE

kVmmVkE

m mkk ne

minus= sum )2(





H0 ψn(0) = E(0) ψn

(0) (H0 + V) ψ = E ψwhere E(0)

n = E(0)n


sum Ψ=Ψn

nn qcq )()( )0()0()0(


(0)(q)





n

( )sumprime

prime =minusn







0

21

22221

11211

=

minus

minusminus

EVVV

VEVVVVEV

NNNN

N

N

L

LLLL

L

L






J JJ

ZZZMJ EE

MJDMJMJDMJMJDMJE

γ γγγ

γγγγγγ 2EE



22


∆

plusmn=∆ γγ2E



M = ndash1

Jrsquo = 1

Jrsquorsquo = 0

M = 0

M = 1

M = 0

e perp Ze perp Z

e Z

ΔM=0

ΔM=plusmn1

σ - component

π - component

σ - component

Z E e





B me

2h


WB = - μ B


M = J J-1 hellip -J


++++minus+

+=JJ

SSLLJJg





Jrsquo = 0

M = 0

M = 1M = 0

e perp Ze perp Z

e ZΔM=0

ΔM=plusmn1

σndash - component

π - component

σ+ - component

Z Н e





dOnMJeJMmc

edW

dOnMJeJMmc

edW

ki

kab

ki

kem

ρρ

ρρ

γγπ

ω

γγπ

ω

2

23

2

2

23

2

2

)1(2

primeprimeprime=

+primeprimeprime=

minus kr

kr

pe

pe

h

h



( )sum +minus=



iii

kind

DM

ksp

DM

mce

dOIMJJMc

dW

dOMJJMc

dW

slM

M

M

22

42

2

2

2

2

3

3

h

r

h

r

h

ωρ

ρ

γmicroγπ

γmicroγπω




sum=



ii

kind

DE

ksp

DE

e

dOIMJJMc

dW

dOMJJMc

dW

rD

De

De

ωρ

ρ

γγπ

γγπω

2

2

2

2

3

3

42

h

h

Selection rules


minus harr minus )

Selection rules



Amn= 1 τ






=

1

2arctannn

Bθ

n1

n2p-polarization



s-polarization





dN2dt = B12

u(ν) N1dN







Albert Einstein





T = 10-εcl



AA NN




I = I0(1 - σ N l)



chBd 0








and ∆νL = γ

τh

asymp∆E

( )2

20 2

21)(

+minus

=γ

γ

πν

vvI




sim 107 sim 10-4


sim10-4 sim 10-15



sim 109 sim 10-2



sim 1012 sim 101


plusmn=

cZ

0v1νν


minus=

Tkm

kTmf

2vexp

2)v(

2Z

Z π


( )

∆minus

minus∆

= 2

202ln4exp12ln4)(

DD

Iννν

νπν where

mTk

cD2ln22 0ν

ν =∆




P12 = P1 + P2


Wavelength λ = hmv


Nobelpreis 1929







φ = φ1+φ2I = |φ1+φ2|2


















5 Dez 1901+ 1 Feb 1976

Hydrogen Atom

reZ

mH e

e 0

22

2


h

2

2

2

2

2

22

zyxe partpart

+partpart

+partpart

=nabla ( )φθ 1 222

2 Λ+

partpart

partpart

=nablar

rrre

( )θ

θθθθθ

φθpartpart

partpart

+partpart

=Λ sinsin

1sin

1 2

2

22

Hamiltonian

Wavefunctions

-

+




Polar coordinates

kkk EH ψψ =


230

10

02aeR

ar

minus

=

230

2

020 22

2 0

a

ear

R

ar

minus

minus

= 230

2

021 62

0

a

ear

R

ar

minus

=




s 0 0 1(4 π)frac12 14 π

p11

plusmn10




d222

plusmn2plusmn10





f

3333




(716 π)frac12 (5 cos3 θ - 3 cos θ)



g

44444















1

2

2




11

s = 1(4p)frac1200

Wave Functions|ml|l



l = 0 m = 0

l = 2






Nobelpreis 1965


K32124

12

0

2

0

=minus= nna

eEnl πε







j = l + s

l s

j = l ndash frac12

j = l + frac12

2

4

3

42

21

)1( h

mellnZE jj +




z-projection


z-projection


TJ

me

eB

24102792

minussdot==h

micro

sBsZ

Bs

lBlZ

Bl

msm

l


micromicro

22minus=

minus=minus=

minus=

rr

rr









Nobelpreis 1945





JS L12 +

oJ

S L12 +

- even states

- odd states

J + J ge 1

S = 1 Triplet state

L = 0 S -state

L = 2 D -state

S = 0 Singlet state

L = 1 P -state


ΔM = 0 plusmn1

M = ndash1

J = 1

J = 0

M = 0

M = 1M = 0

Z

e perp Ze perp Z

e Z

e

ΔM = ndash 1

ΔM=0

ΔM=plusmn1

ΔM = 1



L S

Jmin = |L ndash S|

Jmax = L + SJ+1J

L S

Jmin = |L ndash S|

Jmax = L + SJ+1J

VSO = A LS



А gt 0

А gt 0



J I

Fmin = |J ndash I|

Fmax = J + IF+1F

J I

Fmin = |J ndash I|

Fmax = J + IF+1F

Vhpf = AI JI


Lande interval rule






sum partpartpart

+minus=+=βα βα

αβmicroϕ

micro

2

6)0(

xxQeHWWW Q

F = J + I


H0 ψn(0) = E(0) ψn









sum=n

nn qcq )()( )0(ψψ




kmEE

kVmmVkE

m mkk ne

minus= sum )2(





H0 ψn(0) = E(0) ψn

(0) (H0 + V) ψ = E ψwhere E(0)

n = E(0)n


sum Ψ=Ψn

nn qcq )()( )0()0()0(


(0)(q)





n

( )sumprime

prime =minusn







0

21

22221

11211

=

minus

minusminus

EVVV

VEVVVVEV

NNNN

N

N

L

LLLL

L

L






J JJ

ZZZMJ EE

MJDMJMJDMJMJDMJE

γ γγγ

γγγγγγ 2EE



22


∆

plusmn=∆ γγ2E



M = ndash1

Jrsquo = 1

Jrsquorsquo = 0

M = 0

M = 1

M = 0

e perp Ze perp Z

e Z

ΔM=0

ΔM=plusmn1

σ - component

π - component

σ - component

Z E e





B me

2h


WB = - μ B


M = J J-1 hellip -J


++++minus+

+=JJ

SSLLJJg





Jrsquo = 0

M = 0

M = 1M = 0

e perp Ze perp Z

e ZΔM=0

ΔM=plusmn1

σndash - component

π - component

σ+ - component

Z Н e





dOnMJeJMmc

edW

dOnMJeJMmc

edW

ki

kab

ki

kem

ρρ

ρρ

γγπ

ω

γγπ

ω

2

23

2

2

23

2

2

)1(2

primeprimeprime=

+primeprimeprime=

minus kr

kr

pe

pe

h

h



( )sum +minus=



iii

kind

DM

ksp

DM

mce

dOIMJJMc

dW

dOMJJMc

dW

slM

M

M

22

42

2

2

2

2

3

3

h

r

h

r

h

ωρ

ρ

γmicroγπ

γmicroγπω




sum=



ii

kind

DE

ksp

DE

e

dOIMJJMc

dW

dOMJJMc

dW

rD

De

De

ωρ

ρ

γγπ

γγπω

2

2

2

2

3

3

42

h

h

Selection rules


minus harr minus )

Selection rules



Amn= 1 τ





dN2dt = B12

u(ν) N1dN







Albert Einstein





T = 10-εcl



AA NN




I = I0(1 - σ N l)



chBd 0








and ∆νL = γ

τh

asymp∆E

( )2

20 2

21)(

+minus

=γ

γ

πν

vvI




sim 107 sim 10-4


sim10-4 sim 10-15



sim 109 sim 10-2



sim 1012 sim 101


plusmn=

cZ

0v1νν


minus=

Tkm

kTmf

2vexp

2)v(

2Z

Z π


( )

∆minus

minus∆

= 2

202ln4exp12ln4)(

DD

Iννν

νπν where

mTk

cD2ln22 0ν

ν =∆




P12 = P1 + P2


Wavelength λ = hmv


Nobelpreis 1929







φ = φ1+φ2I = |φ1+φ2|2


















5 Dez 1901+ 1 Feb 1976

Hydrogen Atom

reZ

mH e

e 0

22

2


h

2

2

2

2

2

22

zyxe partpart

+partpart

+partpart

=nabla ( )φθ 1 222

2 Λ+

partpart

partpart

=nablar

rrre

( )θ

θθθθθ

φθpartpart

partpart

+partpart

=Λ sinsin

1sin

1 2

2

22

Hamiltonian

Wavefunctions

-

+




Polar coordinates

kkk EH ψψ =


230

10

02aeR

ar

minus

=

230

2

020 22

2 0

a

ear

R

ar

minus

minus

= 230

2

021 62

0

a

ear

R

ar

minus

=




s 0 0 1(4 π)frac12 14 π

p11

plusmn10




d222

plusmn2plusmn10





f

3333




(716 π)frac12 (5 cos3 θ - 3 cos θ)



g

44444















1

2

2




11

s = 1(4p)frac1200

Wave Functions|ml|l



l = 0 m = 0

l = 2






Nobelpreis 1965


K32124

12

0

2

0

=minus= nna

eEnl πε







j = l + s

l s

j = l ndash frac12

j = l + frac12

2

4

3

42

21

)1( h

mellnZE jj +




z-projection


z-projection


TJ

me

eB

24102792

minussdot==h

micro

sBsZ

Bs

lBlZ

Bl

msm

l


micromicro

22minus=

minus=minus=

minus=

rr

rr









Nobelpreis 1945





JS L12 +

oJ

S L12 +

- even states

- odd states

J + J ge 1

S = 1 Triplet state

L = 0 S -state

L = 2 D -state

S = 0 Singlet state

L = 1 P -state


ΔM = 0 plusmn1

M = ndash1

J = 1

J = 0

M = 0

M = 1M = 0

Z

e perp Ze perp Z

e Z

e

ΔM = ndash 1

ΔM=0

ΔM=plusmn1

ΔM = 1



L S

Jmin = |L ndash S|

Jmax = L + SJ+1J

L S

Jmin = |L ndash S|

Jmax = L + SJ+1J

VSO = A LS



А gt 0

А gt 0



J I

Fmin = |J ndash I|

Fmax = J + IF+1F

J I

Fmin = |J ndash I|

Fmax = J + IF+1F

Vhpf = AI JI


Lande interval rule






sum partpartpart

+minus=+=βα βα

αβmicroϕ

micro

2

6)0(

xxQeHWWW Q

F = J + I


H0 ψn(0) = E(0) ψn









sum=n

nn qcq )()( )0(ψψ




kmEE

kVmmVkE

m mkk ne

minus= sum )2(





H0 ψn(0) = E(0) ψn

(0) (H0 + V) ψ = E ψwhere E(0)

n = E(0)n


sum Ψ=Ψn

nn qcq )()( )0()0()0(


(0)(q)





n

( )sumprime

prime =minusn







0

21

22221

11211

=

minus

minusminus

EVVV

VEVVVVEV

NNNN

N

N

L

LLLL

L

L






J JJ

ZZZMJ EE

MJDMJMJDMJMJDMJE

γ γγγ

γγγγγγ 2EE



22


∆

plusmn=∆ γγ2E



M = ndash1

Jrsquo = 1

Jrsquorsquo = 0

M = 0

M = 1

M = 0

e perp Ze perp Z

e Z

ΔM=0

ΔM=plusmn1

σ - component

π - component

σ - component

Z E e





B me

2h


WB = - μ B


M = J J-1 hellip -J


++++minus+

+=JJ

SSLLJJg





Jrsquo = 0

M = 0

M = 1M = 0

e perp Ze perp Z

e ZΔM=0

ΔM=plusmn1

σndash - component

π - component

σ+ - component

Z Н e





dOnMJeJMmc

edW

dOnMJeJMmc

edW

ki

kab

ki

kem

ρρ

ρρ

γγπ

ω

γγπ

ω

2

23

2

2

23

2

2

)1(2

primeprimeprime=

+primeprimeprime=

minus kr

kr

pe

pe

h

h



( )sum +minus=



iii

kind

DM

ksp

DM

mce

dOIMJJMc

dW

dOMJJMc

dW

slM

M

M

22

42

2

2

2

2

3

3

h

r

h

r

h

ωρ

ρ

γmicroγπ

γmicroγπω




sum=



ii

kind

DE

ksp

DE

e

dOIMJJMc

dW

dOMJJMc

dW

rD

De

De

ωρ

ρ

γγπ

γγπω

2

2

2

2

3

3

42

h

h

Selection rules


minus harr minus )

Selection rules



Amn= 1 τ





Albert Einstein





T = 10-εcl



AA NN




I = I0(1 - σ N l)



chBd 0








and ∆νL = γ

τh

asymp∆E

( )2

20 2

21)(

+minus

=γ

γ

πν

vvI




sim 107 sim 10-4


sim10-4 sim 10-15



sim 109 sim 10-2



sim 1012 sim 101


plusmn=

cZ

0v1νν


minus=

Tkm

kTmf

2vexp

2)v(

2Z

Z π


( )

∆minus

minus∆

= 2

202ln4exp12ln4)(

DD

Iννν

νπν where

mTk

cD2ln22 0ν

ν =∆




P12 = P1 + P2


Wavelength λ = hmv


Nobelpreis 1929







φ = φ1+φ2I = |φ1+φ2|2


















5 Dez 1901+ 1 Feb 1976

Hydrogen Atom

reZ

mH e

e 0

22

2


h

2

2

2

2

2

22

zyxe partpart

+partpart

+partpart

=nabla ( )φθ 1 222

2 Λ+

partpart

partpart

=nablar

rrre

( )θ

θθθθθ

φθpartpart

partpart

+partpart

=Λ sinsin

1sin

1 2

2

22

Hamiltonian

Wavefunctions

-

+




Polar coordinates

kkk EH ψψ =


230

10

02aeR

ar

minus

=

230

2

020 22

2 0

a

ear

R

ar

minus

minus

= 230

2

021 62

0

a

ear

R

ar

minus

=




s 0 0 1(4 π)frac12 14 π

p11

plusmn10




d222

plusmn2plusmn10





f

3333




(716 π)frac12 (5 cos3 θ - 3 cos θ)



g

44444















1

2

2




11

s = 1(4p)frac1200

Wave Functions|ml|l



l = 0 m = 0

l = 2






Nobelpreis 1965


K32124

12

0

2

0

=minus= nna

eEnl πε







j = l + s

l s

j = l ndash frac12

j = l + frac12

2

4

3

42

21

)1( h

mellnZE jj +




z-projection


z-projection


TJ

me

eB

24102792

minussdot==h

micro

sBsZ

Bs

lBlZ

Bl

msm

l


micromicro

22minus=

minus=minus=

minus=

rr

rr









Nobelpreis 1945





JS L12 +

oJ

S L12 +

- even states

- odd states

J + J ge 1

S = 1 Triplet state

L = 0 S -state

L = 2 D -state

S = 0 Singlet state

L = 1 P -state


ΔM = 0 plusmn1

M = ndash1

J = 1

J = 0

M = 0

M = 1M = 0

Z

e perp Ze perp Z

e Z

e

ΔM = ndash 1

ΔM=0

ΔM=plusmn1

ΔM = 1



L S

Jmin = |L ndash S|

Jmax = L + SJ+1J

L S

Jmin = |L ndash S|

Jmax = L + SJ+1J

VSO = A LS



А gt 0

А gt 0



J I

Fmin = |J ndash I|

Fmax = J + IF+1F

J I

Fmin = |J ndash I|

Fmax = J + IF+1F

Vhpf = AI JI


Lande interval rule






sum partpartpart

+minus=+=βα βα

αβmicroϕ

micro

2

6)0(

xxQeHWWW Q

F = J + I


H0 ψn(0) = E(0) ψn









sum=n

nn qcq )()( )0(ψψ




kmEE

kVmmVkE

m mkk ne

minus= sum )2(





H0 ψn(0) = E(0) ψn

(0) (H0 + V) ψ = E ψwhere E(0)

n = E(0)n


sum Ψ=Ψn

nn qcq )()( )0()0()0(


(0)(q)





n

( )sumprime

prime =minusn







0

21

22221

11211

=

minus

minusminus

EVVV

VEVVVVEV

NNNN

N

N

L

LLLL

L

L






J JJ

ZZZMJ EE

MJDMJMJDMJMJDMJE

γ γγγ

γγγγγγ 2EE



22


∆

plusmn=∆ γγ2E



M = ndash1

Jrsquo = 1

Jrsquorsquo = 0

M = 0

M = 1

M = 0

e perp Ze perp Z

e Z

ΔM=0

ΔM=plusmn1

σ - component

π - component

σ - component

Z E e





B me

2h


WB = - μ B


M = J J-1 hellip -J


++++minus+

+=JJ

SSLLJJg





Jrsquo = 0

M = 0

M = 1M = 0

e perp Ze perp Z

e ZΔM=0

ΔM=plusmn1

σndash - component

π - component

σ+ - component

Z Н e





dOnMJeJMmc

edW

dOnMJeJMmc

edW

ki

kab

ki

kem

ρρ

ρρ

γγπ

ω

γγπ

ω

2

23

2

2

23

2

2

)1(2

primeprimeprime=

+primeprimeprime=

minus kr

kr

pe

pe

h

h



( )sum +minus=



iii

kind

DM

ksp

DM

mce

dOIMJJMc

dW

dOMJJMc

dW

slM

M

M

22

42

2

2

2

2

3

3

h

r

h

r

h

ωρ

ρ

γmicroγπ

γmicroγπω




sum=



ii

kind

DE

ksp

DE

e

dOIMJJMc

dW

dOMJJMc

dW

rD

De

De

ωρ

ρ

γγπ

γγπω

2

2

2

2

3

3

42

h

h

Selection rules


minus harr minus )

Selection rules



Amn= 1 τ







T = 10-εcl



AA NN




I = I0(1 - σ N l)



chBd 0








and ∆νL = γ

τh

asymp∆E

( )2

20 2

21)(

+minus

=γ

γ

πν

vvI




sim 107 sim 10-4


sim10-4 sim 10-15



sim 109 sim 10-2



sim 1012 sim 101


plusmn=

cZ

0v1νν


minus=

Tkm

kTmf

2vexp

2)v(

2Z

Z π


( )

∆minus

minus∆

= 2

202ln4exp12ln4)(

DD

Iννν

νπν where

mTk

cD2ln22 0ν

ν =∆




P12 = P1 + P2


Wavelength λ = hmv


Nobelpreis 1929







φ = φ1+φ2I = |φ1+φ2|2


















5 Dez 1901+ 1 Feb 1976

Hydrogen Atom

reZ

mH e

e 0

22

2


h

2

2

2

2

2

22

zyxe partpart

+partpart

+partpart

=nabla ( )φθ 1 222

2 Λ+

partpart

partpart

=nablar

rrre

( )θ

θθθθθ

φθpartpart

partpart

+partpart

=Λ sinsin

1sin

1 2

2

22

Hamiltonian

Wavefunctions

-

+




Polar coordinates

kkk EH ψψ =


230

10

02aeR

ar

minus

=

230

2

020 22

2 0

a

ear

R

ar

minus

minus

= 230

2

021 62

0

a

ear

R

ar

minus

=




s 0 0 1(4 π)frac12 14 π

p11

plusmn10




d222

plusmn2plusmn10





f

3333




(716 π)frac12 (5 cos3 θ - 3 cos θ)



g

44444















1

2

2




11

s = 1(4p)frac1200

Wave Functions|ml|l



l = 0 m = 0

l = 2






Nobelpreis 1965


K32124

12

0

2

0

=minus= nna

eEnl πε







j = l + s

l s

j = l ndash frac12

j = l + frac12

2

4

3

42

21

)1( h

mellnZE jj +




z-projection


z-projection


TJ

me

eB

24102792

minussdot==h

micro

sBsZ

Bs

lBlZ

Bl

msm

l


micromicro

22minus=

minus=minus=

minus=

rr

rr









Nobelpreis 1945





JS L12 +

oJ

S L12 +

- even states

- odd states

J + J ge 1

S = 1 Triplet state

L = 0 S -state

L = 2 D -state

S = 0 Singlet state

L = 1 P -state


ΔM = 0 plusmn1

M = ndash1

J = 1

J = 0

M = 0

M = 1M = 0

Z

e perp Ze perp Z

e Z

e

ΔM = ndash 1

ΔM=0

ΔM=plusmn1

ΔM = 1



L S

Jmin = |L ndash S|

Jmax = L + SJ+1J

L S

Jmin = |L ndash S|

Jmax = L + SJ+1J

VSO = A LS



А gt 0

А gt 0



J I

Fmin = |J ndash I|

Fmax = J + IF+1F

J I

Fmin = |J ndash I|

Fmax = J + IF+1F

Vhpf = AI JI


Lande interval rule






sum partpartpart

+minus=+=βα βα

αβmicroϕ

micro

2

6)0(

xxQeHWWW Q

F = J + I


H0 ψn(0) = E(0) ψn









sum=n

nn qcq )()( )0(ψψ




kmEE

kVmmVkE

m mkk ne

minus= sum )2(





H0 ψn(0) = E(0) ψn

(0) (H0 + V) ψ = E ψwhere E(0)

n = E(0)n


sum Ψ=Ψn

nn qcq )()( )0()0()0(


(0)(q)





n

( )sumprime

prime =minusn







0

21

22221

11211

=

minus

minusminus

EVVV

VEVVVVEV

NNNN

N

N

L

LLLL

L

L






J JJ

ZZZMJ EE

MJDMJMJDMJMJDMJE

γ γγγ

γγγγγγ 2EE



22


∆

plusmn=∆ γγ2E



M = ndash1

Jrsquo = 1

Jrsquorsquo = 0

M = 0

M = 1

M = 0

e perp Ze perp Z

e Z

ΔM=0

ΔM=plusmn1

σ - component

π - component

σ - component

Z E e





B me

2h


WB = - μ B


M = J J-1 hellip -J


++++minus+

+=JJ

SSLLJJg





Jrsquo = 0

M = 0

M = 1M = 0

e perp Ze perp Z

e ZΔM=0

ΔM=plusmn1

σndash - component

π - component

σ+ - component

Z Н e





dOnMJeJMmc

edW

dOnMJeJMmc

edW

ki

kab

ki

kem

ρρ

ρρ

γγπ

ω

γγπ

ω

2

23

2

2

23

2

2

)1(2

primeprimeprime=

+primeprimeprime=

minus kr

kr

pe

pe

h

h



( )sum +minus=



iii

kind

DM

ksp

DM

mce

dOIMJJMc

dW

dOMJJMc

dW

slM

M

M

22

42

2

2

2

2

3

3

h

r

h

r

h

ωρ

ρ

γmicroγπ

γmicroγπω




sum=



ii

kind

DE

ksp

DE

e

dOIMJJMc

dW

dOMJJMc

dW

rD

De

De

ωρ

ρ

γγπ

γγπω

2

2

2

2

3

3

42

h

h

Selection rules


minus harr minus )

Selection rules



Amn= 1 τ





I = I0(1 - σ N l)



chBd 0








and ∆νL = γ

τh

asymp∆E

( )2

20 2

21)(

+minus

=γ

γ

πν

vvI




sim 107 sim 10-4


sim10-4 sim 10-15



sim 109 sim 10-2



sim 1012 sim 101


plusmn=

cZ

0v1νν


minus=

Tkm

kTmf

2vexp

2)v(

2Z

Z π


( )

∆minus

minus∆

= 2

202ln4exp12ln4)(

DD

Iννν

νπν where

mTk

cD2ln22 0ν

ν =∆




P12 = P1 + P2


Wavelength λ = hmv


Nobelpreis 1929







φ = φ1+φ2I = |φ1+φ2|2


















5 Dez 1901+ 1 Feb 1976

Hydrogen Atom

reZ

mH e

e 0

22

2


h

2

2

2

2

2

22

zyxe partpart

+partpart

+partpart

=nabla ( )φθ 1 222

2 Λ+

partpart

partpart

=nablar

rrre

( )θ

θθθθθ

φθpartpart

partpart

+partpart

=Λ sinsin

1sin

1 2

2

22

Hamiltonian

Wavefunctions

-

+




Polar coordinates

kkk EH ψψ =


230

10

02aeR

ar

minus

=

230

2

020 22

2 0

a

ear

R

ar

minus

minus

= 230

2

021 62

0

a

ear

R

ar

minus

=




s 0 0 1(4 π)frac12 14 π

p11

plusmn10




d222

plusmn2plusmn10





f

3333




(716 π)frac12 (5 cos3 θ - 3 cos θ)



g

44444















1

2

2




11

s = 1(4p)frac1200

Wave Functions|ml|l



l = 0 m = 0

l = 2






Nobelpreis 1965


K32124

12

0

2

0

=minus= nna

eEnl πε







j = l + s

l s

j = l ndash frac12

j = l + frac12

2

4

3

42

21

)1( h

mellnZE jj +




z-projection


z-projection


TJ

me

eB

24102792

minussdot==h

micro

sBsZ

Bs

lBlZ

Bl

msm

l


micromicro

22minus=

minus=minus=

minus=

rr

rr









Nobelpreis 1945





JS L12 +

oJ

S L12 +

- even states

- odd states

J + J ge 1

S = 1 Triplet state

L = 0 S -state

L = 2 D -state

S = 0 Singlet state

L = 1 P -state


ΔM = 0 plusmn1

M = ndash1

J = 1

J = 0

M = 0

M = 1M = 0

Z

e perp Ze perp Z

e Z

e

ΔM = ndash 1

ΔM=0

ΔM=plusmn1

ΔM = 1



L S

Jmin = |L ndash S|

Jmax = L + SJ+1J

L S

Jmin = |L ndash S|

Jmax = L + SJ+1J

VSO = A LS



А gt 0

А gt 0



J I

Fmin = |J ndash I|

Fmax = J + IF+1F

J I

Fmin = |J ndash I|

Fmax = J + IF+1F

Vhpf = AI JI


Lande interval rule






sum partpartpart

+minus=+=βα βα

αβmicroϕ

micro

2

6)0(

xxQeHWWW Q

F = J + I


H0 ψn(0) = E(0) ψn









sum=n

nn qcq )()( )0(ψψ




kmEE

kVmmVkE

m mkk ne

minus= sum )2(





H0 ψn(0) = E(0) ψn

(0) (H0 + V) ψ = E ψwhere E(0)

n = E(0)n


sum Ψ=Ψn

nn qcq )()( )0()0()0(


(0)(q)





n

( )sumprime

prime =minusn







0

21

22221

11211

=

minus

minusminus

EVVV

VEVVVVEV

NNNN

N

N

L

LLLL

L

L






J JJ

ZZZMJ EE

MJDMJMJDMJMJDMJE

γ γγγ

γγγγγγ 2EE



22


∆

plusmn=∆ γγ2E



M = ndash1

Jrsquo = 1

Jrsquorsquo = 0

M = 0

M = 1

M = 0

e perp Ze perp Z

e Z

ΔM=0

ΔM=plusmn1

σ - component

π - component

σ - component

Z E e





B me

2h


WB = - μ B


M = J J-1 hellip -J


++++minus+

+=JJ

SSLLJJg





Jrsquo = 0

M = 0

M = 1M = 0

e perp Ze perp Z

e ZΔM=0

ΔM=plusmn1

σndash - component

π - component

σ+ - component

Z Н e





dOnMJeJMmc

edW

dOnMJeJMmc

edW

ki

kab

ki

kem

ρρ

ρρ

γγπ

ω

γγπ

ω

2

23

2

2

23

2

2

)1(2

primeprimeprime=

+primeprimeprime=

minus kr

kr

pe

pe

h

h



( )sum +minus=



iii

kind

DM

ksp

DM

mce

dOIMJJMc

dW

dOMJJMc

dW

slM

M

M

22

42

2

2

2

2

3

3

h

r

h

r

h

ωρ

ρ

γmicroγπ

γmicroγπω




sum=



ii

kind

DE

ksp

DE

e

dOIMJJMc

dW

dOMJJMc

dW

rD

De

De

ωρ

ρ

γγπ

γγπω

2

2

2

2

3

3

42

h

h

Selection rules


minus harr minus )

Selection rules



Amn= 1 τ









and ∆νL = γ

τh

asymp∆E

( )2

20 2

21)(

+minus

=γ

γ

πν

vvI




sim 107 sim 10-4


sim10-4 sim 10-15



sim 109 sim 10-2



sim 1012 sim 101


plusmn=

cZ

0v1νν


minus=

Tkm

kTmf

2vexp

2)v(

2Z

Z π


( )

∆minus

minus∆

= 2

202ln4exp12ln4)(

DD

Iννν

νπν where

mTk

cD2ln22 0ν

ν =∆




P12 = P1 + P2


Wavelength λ = hmv


Nobelpreis 1929







φ = φ1+φ2I = |φ1+φ2|2


















5 Dez 1901+ 1 Feb 1976

Hydrogen Atom

reZ

mH e

e 0

22

2


h

2

2

2

2

2

22

zyxe partpart

+partpart

+partpart

=nabla ( )φθ 1 222

2 Λ+

partpart

partpart

=nablar

rrre

( )θ

θθθθθ

φθpartpart

partpart

+partpart

=Λ sinsin

1sin

1 2

2

22

Hamiltonian

Wavefunctions

-

+




Polar coordinates

kkk EH ψψ =


230

10

02aeR

ar

minus

=

230

2

020 22

2 0

a

ear

R

ar

minus

minus

= 230

2

021 62

0

a

ear

R

ar

minus

=




s 0 0 1(4 π)frac12 14 π

p11

plusmn10




d222

plusmn2plusmn10





f

3333




(716 π)frac12 (5 cos3 θ - 3 cos θ)



g

44444















1

2

2




11

s = 1(4p)frac1200

Wave Functions|ml|l



l = 0 m = 0

l = 2






Nobelpreis 1965


K32124

12

0

2

0

=minus= nna

eEnl πε







j = l + s

l s

j = l ndash frac12

j = l + frac12

2

4

3

42

21

)1( h

mellnZE jj +




z-projection


z-projection


TJ

me

eB

24102792

minussdot==h

micro

sBsZ

Bs

lBlZ

Bl

msm

l


micromicro

22minus=

minus=minus=

minus=

rr

rr









Nobelpreis 1945





JS L12 +

oJ

S L12 +

- even states

- odd states

J + J ge 1

S = 1 Triplet state

L = 0 S -state

L = 2 D -state

S = 0 Singlet state

L = 1 P -state


ΔM = 0 plusmn1

M = ndash1

J = 1

J = 0

M = 0

M = 1M = 0

Z

e perp Ze perp Z

e Z

e

ΔM = ndash 1

ΔM=0

ΔM=plusmn1

ΔM = 1



L S

Jmin = |L ndash S|

Jmax = L + SJ+1J

L S

Jmin = |L ndash S|

Jmax = L + SJ+1J

VSO = A LS



А gt 0

А gt 0



J I

Fmin = |J ndash I|

Fmax = J + IF+1F

J I

Fmin = |J ndash I|

Fmax = J + IF+1F

Vhpf = AI JI


Lande interval rule






sum partpartpart

+minus=+=βα βα

αβmicroϕ

micro

2

6)0(

xxQeHWWW Q

F = J + I


H0 ψn(0) = E(0) ψn









sum=n

nn qcq )()( )0(ψψ




kmEE

kVmmVkE

m mkk ne

minus= sum )2(





H0 ψn(0) = E(0) ψn

(0) (H0 + V) ψ = E ψwhere E(0)

n = E(0)n


sum Ψ=Ψn

nn qcq )()( )0()0()0(


(0)(q)





n

( )sumprime

prime =minusn







0

21

22221

11211

=

minus

minusminus

EVVV

VEVVVVEV

NNNN

N

N

L

LLLL

L

L






J JJ

ZZZMJ EE

MJDMJMJDMJMJDMJE

γ γγγ

γγγγγγ 2EE



22


∆

plusmn=∆ γγ2E



M = ndash1

Jrsquo = 1

Jrsquorsquo = 0

M = 0

M = 1

M = 0

e perp Ze perp Z

e Z

ΔM=0

ΔM=plusmn1

σ - component

π - component

σ - component

Z E e





B me

2h


WB = - μ B


M = J J-1 hellip -J


++++minus+

+=JJ

SSLLJJg





Jrsquo = 0

M = 0

M = 1M = 0

e perp Ze perp Z

e ZΔM=0

ΔM=plusmn1

σndash - component

π - component

σ+ - component

Z Н e





dOnMJeJMmc

edW

dOnMJeJMmc

edW

ki

kab

ki

kem

ρρ

ρρ

γγπ

ω

γγπ

ω

2

23

2

2

23

2

2

)1(2

primeprimeprime=

+primeprimeprime=

minus kr

kr

pe

pe

h

h



( )sum +minus=



iii

kind

DM

ksp

DM

mce

dOIMJJMc

dW

dOMJJMc

dW

slM

M

M

22

42

2

2

2

2

3

3

h

r

h

r

h

ωρ

ρ

γmicroγπ

γmicroγπω




sum=



ii

kind

DE

ksp

DE

e

dOIMJJMc

dW

dOMJJMc

dW

rD

De

De

ωρ

ρ

γγπ

γγπω

2

2

2

2

3

3

42

h

h

Selection rules


minus harr minus )

Selection rules



Amn= 1 τ






sim 107 sim 10-4


sim10-4 sim 10-15



sim 109 sim 10-2



sim 1012 sim 101


plusmn=

cZ

0v1νν


minus=

Tkm

kTmf

2vexp

2)v(

2Z

Z π


( )

∆minus

minus∆

= 2

202ln4exp12ln4)(

DD

Iννν

νπν where

mTk

cD2ln22 0ν

ν =∆




P12 = P1 + P2


Wavelength λ = hmv


Nobelpreis 1929







φ = φ1+φ2I = |φ1+φ2|2


















5 Dez 1901+ 1 Feb 1976

Hydrogen Atom

reZ

mH e

e 0

22

2


h

2

2

2

2

2

22

zyxe partpart

+partpart

+partpart

=nabla ( )φθ 1 222

2 Λ+

partpart

partpart

=nablar

rrre

( )θ

θθθθθ

φθpartpart

partpart

+partpart

=Λ sinsin

1sin

1 2

2

22

Hamiltonian

Wavefunctions

-

+




Polar coordinates

kkk EH ψψ =


230

10

02aeR

ar

minus

=

230

2

020 22

2 0

a

ear

R

ar

minus

minus

= 230

2

021 62

0

a

ear

R

ar

minus

=




s 0 0 1(4 π)frac12 14 π

p11

plusmn10




d222

plusmn2plusmn10





f

3333




(716 π)frac12 (5 cos3 θ - 3 cos θ)



g

44444















1

2

2




11

s = 1(4p)frac1200

Wave Functions|ml|l



l = 0 m = 0

l = 2






Nobelpreis 1965


K32124

12

0

2

0

=minus= nna

eEnl πε







j = l + s

l s

j = l ndash frac12

j = l + frac12

2

4

3

42

21

)1( h

mellnZE jj +




z-projection


z-projection


TJ

me

eB

24102792

minussdot==h

micro

sBsZ

Bs

lBlZ

Bl

msm

l


micromicro

22minus=

minus=minus=

minus=

rr

rr









Nobelpreis 1945





JS L12 +

oJ

S L12 +

- even states

- odd states

J + J ge 1

S = 1 Triplet state

L = 0 S -state

L = 2 D -state

S = 0 Singlet state

L = 1 P -state


ΔM = 0 plusmn1

M = ndash1

J = 1

J = 0

M = 0

M = 1M = 0

Z

e perp Ze perp Z

e Z

e

ΔM = ndash 1

ΔM=0

ΔM=plusmn1

ΔM = 1



L S

Jmin = |L ndash S|

Jmax = L + SJ+1J

L S

Jmin = |L ndash S|

Jmax = L + SJ+1J

VSO = A LS



А gt 0

А gt 0



J I

Fmin = |J ndash I|

Fmax = J + IF+1F

J I

Fmin = |J ndash I|

Fmax = J + IF+1F

Vhpf = AI JI


Lande interval rule






sum partpartpart

+minus=+=βα βα

αβmicroϕ

micro

2

6)0(

xxQeHWWW Q

F = J + I


H0 ψn(0) = E(0) ψn









sum=n

nn qcq )()( )0(ψψ




kmEE

kVmmVkE

m mkk ne

minus= sum )2(





H0 ψn(0) = E(0) ψn

(0) (H0 + V) ψ = E ψwhere E(0)

n = E(0)n


sum Ψ=Ψn

nn qcq )()( )0()0()0(


(0)(q)





n

( )sumprime

prime =minusn







0

21

22221

11211

=

minus

minusminus

EVVV

VEVVVVEV

NNNN

N

N

L

LLLL

L

L






J JJ

ZZZMJ EE

MJDMJMJDMJMJDMJE

γ γγγ

γγγγγγ 2EE



22


∆

plusmn=∆ γγ2E



M = ndash1

Jrsquo = 1

Jrsquorsquo = 0

M = 0

M = 1

M = 0

e perp Ze perp Z

e Z

ΔM=0

ΔM=plusmn1

σ - component

π - component

σ - component

Z E e





B me

2h


WB = - μ B


M = J J-1 hellip -J


++++minus+

+=JJ

SSLLJJg





Jrsquo = 0

M = 0

M = 1M = 0

e perp Ze perp Z

e ZΔM=0

ΔM=plusmn1

σndash - component

π - component

σ+ - component

Z Н e





dOnMJeJMmc

edW

dOnMJeJMmc

edW

ki

kab

ki

kem

ρρ

ρρ

γγπ

ω

γγπ

ω

2

23

2

2

23

2

2

)1(2

primeprimeprime=

+primeprimeprime=

minus kr

kr

pe

pe

h

h



( )sum +minus=



iii

kind

DM

ksp

DM

mce

dOIMJJMc

dW

dOMJJMc

dW

slM

M

M

22

42

2

2

2

2

3

3

h

r

h

r

h

ωρ

ρ

γmicroγπ

γmicroγπω




sum=



ii

kind

DE

ksp

DE

e

dOIMJJMc

dW

dOMJJMc

dW

rD

De

De

ωρ

ρ

γγπ

γγπω

2

2

2

2

3

3

42

h

h

Selection rules


minus harr minus )

Selection rules



Amn= 1 τ




plusmn=

cZ

0v1νν


minus=

Tkm

kTmf

2vexp

2)v(

2Z

Z π


( )

∆minus

minus∆

= 2

202ln4exp12ln4)(

DD

Iννν

νπν where

mTk

cD2ln22 0ν

ν =∆




P12 = P1 + P2


Wavelength λ = hmv


Nobelpreis 1929







φ = φ1+φ2I = |φ1+φ2|2


















5 Dez 1901+ 1 Feb 1976

Hydrogen Atom

reZ

mH e

e 0

22

2


h

2

2

2

2

2

22

zyxe partpart

+partpart

+partpart

=nabla ( )φθ 1 222

2 Λ+

partpart

partpart

=nablar

rrre

( )θ

θθθθθ

φθpartpart

partpart

+partpart

=Λ sinsin

1sin

1 2

2

22

Hamiltonian

Wavefunctions

-

+




Polar coordinates

kkk EH ψψ =


230

10

02aeR

ar

minus

=

230

2

020 22

2 0

a

ear

R

ar

minus

minus

= 230

2

021 62

0

a

ear

R

ar

minus

=




s 0 0 1(4 π)frac12 14 π

p11

plusmn10




d222

plusmn2plusmn10





f

3333




(716 π)frac12 (5 cos3 θ - 3 cos θ)



g

44444















1

2

2




11

s = 1(4p)frac1200

Wave Functions|ml|l



l = 0 m = 0

l = 2






Nobelpreis 1965


K32124

12

0

2

0

=minus= nna

eEnl πε







j = l + s

l s

j = l ndash frac12

j = l + frac12

2

4

3

42

21

)1( h

mellnZE jj +




z-projection


z-projection


TJ

me

eB

24102792

minussdot==h

micro

sBsZ

Bs

lBlZ

Bl

msm

l


micromicro

22minus=

minus=minus=

minus=

rr

rr









Nobelpreis 1945





JS L12 +

oJ

S L12 +

- even states

- odd states

J + J ge 1

S = 1 Triplet state

L = 0 S -state

L = 2 D -state

S = 0 Singlet state

L = 1 P -state


ΔM = 0 plusmn1

M = ndash1

J = 1

J = 0

M = 0

M = 1M = 0

Z

e perp Ze perp Z

e Z

e

ΔM = ndash 1

ΔM=0

ΔM=plusmn1

ΔM = 1



L S

Jmin = |L ndash S|

Jmax = L + SJ+1J

L S

Jmin = |L ndash S|

Jmax = L + SJ+1J

VSO = A LS



А gt 0

А gt 0



J I

Fmin = |J ndash I|

Fmax = J + IF+1F

J I

Fmin = |J ndash I|

Fmax = J + IF+1F

Vhpf = AI JI


Lande interval rule






sum partpartpart

+minus=+=βα βα

αβmicroϕ

micro

2

6)0(

xxQeHWWW Q

F = J + I


H0 ψn(0) = E(0) ψn









sum=n

nn qcq )()( )0(ψψ




kmEE

kVmmVkE

m mkk ne

minus= sum )2(





H0 ψn(0) = E(0) ψn

(0) (H0 + V) ψ = E ψwhere E(0)

n = E(0)n


sum Ψ=Ψn

nn qcq )()( )0()0()0(


(0)(q)





n

( )sumprime

prime =minusn







0

21

22221

11211

=

minus

minusminus

EVVV

VEVVVVEV

NNNN

N

N

L

LLLL

L

L






J JJ

ZZZMJ EE

MJDMJMJDMJMJDMJE

γ γγγ

γγγγγγ 2EE



22


∆

plusmn=∆ γγ2E



M = ndash1

Jrsquo = 1

Jrsquorsquo = 0

M = 0

M = 1

M = 0

e perp Ze perp Z

e Z

ΔM=0

ΔM=plusmn1

σ - component

π - component

σ - component

Z E e





B me

2h


WB = - μ B


M = J J-1 hellip -J


++++minus+

+=JJ

SSLLJJg





Jrsquo = 0

M = 0

M = 1M = 0

e perp Ze perp Z

e ZΔM=0

ΔM=plusmn1

σndash - component

π - component

σ+ - component

Z Н e





dOnMJeJMmc

edW

dOnMJeJMmc

edW

ki

kab

ki

kem

ρρ

ρρ

γγπ

ω

γγπ

ω

2

23

2

2

23

2

2

)1(2

primeprimeprime=

+primeprimeprime=

minus kr

kr

pe

pe

h

h



( )sum +minus=



iii

kind

DM

ksp

DM

mce

dOIMJJMc

dW

dOMJJMc

dW

slM

M

M

22

42

2

2

2

2

3

3

h

r

h

r

h

ωρ

ρ

γmicroγπ

γmicroγπω




sum=



ii

kind

DE

ksp

DE

e

dOIMJJMc

dW

dOMJJMc

dW

rD

De

De

ωρ

ρ

γγπ

γγπω

2

2

2

2

3

3

42

h

h

Selection rules


minus harr minus )

Selection rules



Amn= 1 τ





P12 = P1 + P2


Wavelength λ = hmv


Nobelpreis 1929







φ = φ1+φ2I = |φ1+φ2|2


















5 Dez 1901+ 1 Feb 1976

Hydrogen Atom

reZ

mH e

e 0

22

2


h

2

2

2

2

2

22

zyxe partpart

+partpart

+partpart

=nabla ( )φθ 1 222

2 Λ+

partpart

partpart

=nablar

rrre

( )θ

θθθθθ

φθpartpart

partpart

+partpart

=Λ sinsin

1sin

1 2

2

22

Hamiltonian

Wavefunctions

-

+




Polar coordinates

kkk EH ψψ =


230

10

02aeR

ar

minus

=

230

2

020 22

2 0

a

ear

R

ar

minus

minus

= 230

2

021 62

0

a

ear

R

ar

minus

=




s 0 0 1(4 π)frac12 14 π

p11

plusmn10




d222

plusmn2plusmn10





f

3333




(716 π)frac12 (5 cos3 θ - 3 cos θ)



g

44444















1

2

2




11

s = 1(4p)frac1200

Wave Functions|ml|l



l = 0 m = 0

l = 2






Nobelpreis 1965


K32124

12

0

2

0

=minus= nna

eEnl πε







j = l + s

l s

j = l ndash frac12

j = l + frac12

2

4

3

42

21

)1( h

mellnZE jj +




z-projection


z-projection


TJ

me

eB

24102792

minussdot==h

micro

sBsZ

Bs

lBlZ

Bl

msm

l


micromicro

22minus=

minus=minus=

minus=

rr

rr









Nobelpreis 1945





JS L12 +

oJ

S L12 +

- even states

- odd states

J + J ge 1

S = 1 Triplet state

L = 0 S -state

L = 2 D -state

S = 0 Singlet state

L = 1 P -state


ΔM = 0 plusmn1

M = ndash1

J = 1

J = 0

M = 0

M = 1M = 0

Z

e perp Ze perp Z

e Z

e

ΔM = ndash 1

ΔM=0

ΔM=plusmn1

ΔM = 1



L S

Jmin = |L ndash S|

Jmax = L + SJ+1J

L S

Jmin = |L ndash S|

Jmax = L + SJ+1J

VSO = A LS



А gt 0

А gt 0



J I

Fmin = |J ndash I|

Fmax = J + IF+1F

J I

Fmin = |J ndash I|

Fmax = J + IF+1F

Vhpf = AI JI


Lande interval rule






sum partpartpart

+minus=+=βα βα

αβmicroϕ

micro

2

6)0(

xxQeHWWW Q

F = J + I


H0 ψn(0) = E(0) ψn









sum=n

nn qcq )()( )0(ψψ




kmEE

kVmmVkE

m mkk ne

minus= sum )2(





H0 ψn(0) = E(0) ψn

(0) (H0 + V) ψ = E ψwhere E(0)

n = E(0)n


sum Ψ=Ψn

nn qcq )()( )0()0()0(


(0)(q)





n

( )sumprime

prime =minusn







0

21

22221

11211

=

minus

minusminus

EVVV

VEVVVVEV

NNNN

N

N

L

LLLL

L

L






J JJ

ZZZMJ EE

MJDMJMJDMJMJDMJE

γ γγγ

γγγγγγ 2EE



22


∆

plusmn=∆ γγ2E



M = ndash1

Jrsquo = 1

Jrsquorsquo = 0

M = 0

M = 1

M = 0

e perp Ze perp Z

e Z

ΔM=0

ΔM=plusmn1

σ - component

π - component

σ - component

Z E e





B me

2h


WB = - μ B


M = J J-1 hellip -J


++++minus+

+=JJ

SSLLJJg





Jrsquo = 0

M = 0

M = 1M = 0

e perp Ze perp Z

e ZΔM=0

ΔM=plusmn1

σndash - component

π - component

σ+ - component

Z Н e





dOnMJeJMmc

edW

dOnMJeJMmc

edW

ki

kab

ki

kem

ρρ

ρρ

γγπ

ω

γγπ

ω

2

23

2

2

23

2

2

)1(2

primeprimeprime=

+primeprimeprime=

minus kr

kr

pe

pe

h

h



( )sum +minus=



iii

kind

DM

ksp

DM

mce

dOIMJJMc

dW

dOMJJMc

dW

slM

M

M

22

42

2

2

2

2

3

3

h

r

h

r

h

ωρ

ρ

γmicroγπ

γmicroγπω




sum=



ii

kind

DE

ksp

DE

e

dOIMJJMc

dW

dOMJJMc

dW

rD

De

De

ωρ

ρ

γγπ

γγπω

2

2

2

2

3

3

42

h

h

Selection rules


minus harr minus )

Selection rules



Amn= 1 τ




Wavelength λ = hmv


Nobelpreis 1929







φ = φ1+φ2I = |φ1+φ2|2


















5 Dez 1901+ 1 Feb 1976

Hydrogen Atom

reZ

mH e

e 0

22

2


h

2

2

2

2

2

22

zyxe partpart

+partpart

+partpart

=nabla ( )φθ 1 222

2 Λ+

partpart

partpart

=nablar

rrre

( )θ

θθθθθ

φθpartpart

partpart

+partpart

=Λ sinsin

1sin

1 2

2

22

Hamiltonian

Wavefunctions

-

+




Polar coordinates

kkk EH ψψ =


230

10

02aeR

ar

minus

=

230

2

020 22

2 0

a

ear

R

ar

minus

minus

= 230

2

021 62

0

a

ear

R

ar

minus

=




s 0 0 1(4 π)frac12 14 π

p11

plusmn10




d222

plusmn2plusmn10





f

3333




(716 π)frac12 (5 cos3 θ - 3 cos θ)



g

44444















1

2

2




11

s = 1(4p)frac1200

Wave Functions|ml|l



l = 0 m = 0

l = 2






Nobelpreis 1965


K32124

12

0

2

0

=minus= nna

eEnl πε







j = l + s

l s

j = l ndash frac12

j = l + frac12

2

4

3

42

21

)1( h

mellnZE jj +




z-projection


z-projection


TJ

me

eB

24102792

minussdot==h

micro

sBsZ

Bs

lBlZ

Bl

msm

l


micromicro

22minus=

minus=minus=

minus=

rr

rr









Nobelpreis 1945





JS L12 +

oJ

S L12 +

- even states

- odd states

J + J ge 1

S = 1 Triplet state

L = 0 S -state

L = 2 D -state

S = 0 Singlet state

L = 1 P -state


ΔM = 0 plusmn1

M = ndash1

J = 1

J = 0

M = 0

M = 1M = 0

Z

e perp Ze perp Z

e Z

e

ΔM = ndash 1

ΔM=0

ΔM=plusmn1

ΔM = 1



L S

Jmin = |L ndash S|

Jmax = L + SJ+1J

L S

Jmin = |L ndash S|

Jmax = L + SJ+1J

VSO = A LS



А gt 0

А gt 0



J I

Fmin = |J ndash I|

Fmax = J + IF+1F

J I

Fmin = |J ndash I|

Fmax = J + IF+1F

Vhpf = AI JI


Lande interval rule






sum partpartpart

+minus=+=βα βα

αβmicroϕ

micro

2

6)0(

xxQeHWWW Q

F = J + I


H0 ψn(0) = E(0) ψn









sum=n

nn qcq )()( )0(ψψ




kmEE

kVmmVkE

m mkk ne

minus= sum )2(





H0 ψn(0) = E(0) ψn

(0) (H0 + V) ψ = E ψwhere E(0)

n = E(0)n


sum Ψ=Ψn

nn qcq )()( )0()0()0(


(0)(q)





n

( )sumprime

prime =minusn







0

21

22221

11211

=

minus

minusminus

EVVV

VEVVVVEV

NNNN

N

N

L

LLLL

L

L






J JJ

ZZZMJ EE

MJDMJMJDMJMJDMJE

γ γγγ

γγγγγγ 2EE



22


∆

plusmn=∆ γγ2E



M = ndash1

Jrsquo = 1

Jrsquorsquo = 0

M = 0

M = 1

M = 0

e perp Ze perp Z

e Z

ΔM=0

ΔM=plusmn1

σ - component

π - component

σ - component

Z E e





B me

2h


WB = - μ B


M = J J-1 hellip -J


++++minus+

+=JJ

SSLLJJg





Jrsquo = 0

M = 0

M = 1M = 0

e perp Ze perp Z

e ZΔM=0

ΔM=plusmn1

σndash - component

π - component

σ+ - component

Z Н e





dOnMJeJMmc

edW

dOnMJeJMmc

edW

ki

kab

ki

kem

ρρ

ρρ

γγπ

ω

γγπ

ω

2

23

2

2

23

2

2

)1(2

primeprimeprime=

+primeprimeprime=

minus kr

kr

pe

pe

h

h



( )sum +minus=



iii

kind

DM

ksp

DM

mce

dOIMJJMc

dW

dOMJJMc

dW

slM

M

M

22

42

2

2

2

2

3

3

h

r

h

r

h

ωρ

ρ

γmicroγπ

γmicroγπω




sum=



ii

kind

DE

ksp

DE

e

dOIMJJMc

dW

dOMJJMc

dW

rD

De

De

ωρ

ρ

γγπ

γγπω

2

2

2

2

3

3

42

h

h

Selection rules


minus harr minus )

Selection rules



Amn= 1 τ








φ = φ1+φ2I = |φ1+φ2|2


















5 Dez 1901+ 1 Feb 1976

Hydrogen Atom

reZ

mH e

e 0

22

2


h

2

2

2

2

2

22

zyxe partpart

+partpart

+partpart

=nabla ( )φθ 1 222

2 Λ+

partpart

partpart

=nablar

rrre

( )θ

θθθθθ

φθpartpart

partpart

+partpart

=Λ sinsin

1sin

1 2

2

22

Hamiltonian

Wavefunctions

-

+




Polar coordinates

kkk EH ψψ =


230

10

02aeR

ar

minus

=

230

2

020 22

2 0

a

ear

R

ar

minus

minus

= 230

2

021 62

0

a

ear

R

ar

minus

=




s 0 0 1(4 π)frac12 14 π

p11

plusmn10




d222

plusmn2plusmn10





f

3333




(716 π)frac12 (5 cos3 θ - 3 cos θ)



g

44444















1

2

2




11

s = 1(4p)frac1200

Wave Functions|ml|l



l = 0 m = 0

l = 2






Nobelpreis 1965


K32124

12

0

2

0

=minus= nna

eEnl πε







j = l + s

l s

j = l ndash frac12

j = l + frac12

2

4

3

42

21

)1( h

mellnZE jj +




z-projection


z-projection


TJ

me

eB

24102792

minussdot==h

micro

sBsZ

Bs

lBlZ

Bl

msm

l


micromicro

22minus=

minus=minus=

minus=

rr

rr









Nobelpreis 1945





JS L12 +

oJ

S L12 +

- even states

- odd states

J + J ge 1

S = 1 Triplet state

L = 0 S -state

L = 2 D -state

S = 0 Singlet state

L = 1 P -state


ΔM = 0 plusmn1

M = ndash1

J = 1

J = 0

M = 0

M = 1M = 0

Z

e perp Ze perp Z

e Z

e

ΔM = ndash 1

ΔM=0

ΔM=plusmn1

ΔM = 1



L S

Jmin = |L ndash S|

Jmax = L + SJ+1J

L S

Jmin = |L ndash S|

Jmax = L + SJ+1J

VSO = A LS



А gt 0

А gt 0



J I

Fmin = |J ndash I|

Fmax = J + IF+1F

J I

Fmin = |J ndash I|

Fmax = J + IF+1F

Vhpf = AI JI


Lande interval rule






sum partpartpart

+minus=+=βα βα

αβmicroϕ

micro

2

6)0(

xxQeHWWW Q

F = J + I


H0 ψn(0) = E(0) ψn









sum=n

nn qcq )()( )0(ψψ




kmEE

kVmmVkE

m mkk ne

minus= sum )2(





H0 ψn(0) = E(0) ψn

(0) (H0 + V) ψ = E ψwhere E(0)

n = E(0)n


sum Ψ=Ψn

nn qcq )()( )0()0()0(


(0)(q)





n

( )sumprime

prime =minusn







0

21

22221

11211

=

minus

minusminus

EVVV

VEVVVVEV

NNNN

N

N

L

LLLL

L

L






J JJ

ZZZMJ EE

MJDMJMJDMJMJDMJE

γ γγγ

γγγγγγ 2EE



22


∆

plusmn=∆ γγ2E



M = ndash1

Jrsquo = 1

Jrsquorsquo = 0

M = 0

M = 1

M = 0

e perp Ze perp Z

e Z

ΔM=0

ΔM=plusmn1

σ - component

π - component

σ - component

Z E e





B me

2h


WB = - μ B


M = J J-1 hellip -J


++++minus+

+=JJ

SSLLJJg





Jrsquo = 0

M = 0

M = 1M = 0

e perp Ze perp Z

e ZΔM=0

ΔM=plusmn1

σndash - component

π - component

σ+ - component

Z Н e





dOnMJeJMmc

edW

dOnMJeJMmc

edW

ki

kab

ki

kem

ρρ

ρρ

γγπ

ω

γγπ

ω

2

23

2

2

23

2

2

)1(2

primeprimeprime=

+primeprimeprime=

minus kr

kr

pe

pe

h

h



( )sum +minus=



iii

kind

DM

ksp

DM

mce

dOIMJJMc

dW

dOMJJMc

dW

slM

M

M

22

42

2

2

2

2

3

3

h

r

h

r

h

ωρ

ρ

γmicroγπ

γmicroγπω




sum=



ii

kind

DE

ksp

DE

e

dOIMJJMc

dW

dOMJJMc

dW

rD

De

De

ωρ

ρ

γγπ

γγπω

2

2

2

2

3

3

42

h

h

Selection rules


minus harr minus )

Selection rules



Amn= 1 τ


















5 Dez 1901+ 1 Feb 1976

Hydrogen Atom

reZ

mH e

e 0

22

2


h

2

2

2

2

2

22

zyxe partpart

+partpart

+partpart

=nabla ( )φθ 1 222

2 Λ+

partpart

partpart

=nablar

rrre

( )θ

θθθθθ

φθpartpart

partpart

+partpart

=Λ sinsin

1sin

1 2

2

22

Hamiltonian

Wavefunctions

-

+




Polar coordinates

kkk EH ψψ =


230

10

02aeR

ar

minus

=

230

2

020 22

2 0

a

ear

R

ar

minus

minus

= 230

2

021 62

0

a

ear

R

ar

minus

=




s 0 0 1(4 π)frac12 14 π

p11

plusmn10




d222

plusmn2plusmn10





f

3333




(716 π)frac12 (5 cos3 θ - 3 cos θ)



g

44444















1

2

2




11

s = 1(4p)frac1200

Wave Functions|ml|l



l = 0 m = 0

l = 2






Nobelpreis 1965


K32124

12

0

2

0

=minus= nna

eEnl πε







j = l + s

l s

j = l ndash frac12

j = l + frac12

2

4

3

42

21

)1( h

mellnZE jj +




z-projection


z-projection


TJ

me

eB

24102792

minussdot==h

micro

sBsZ

Bs

lBlZ

Bl

msm

l


micromicro

22minus=

minus=minus=

minus=

rr

rr









Nobelpreis 1945





JS L12 +

oJ

S L12 +

- even states

- odd states

J + J ge 1

S = 1 Triplet state

L = 0 S -state

L = 2 D -state

S = 0 Singlet state

L = 1 P -state


ΔM = 0 plusmn1

M = ndash1

J = 1

J = 0

M = 0

M = 1M = 0

Z

e perp Ze perp Z

e Z

e

ΔM = ndash 1

ΔM=0

ΔM=plusmn1

ΔM = 1



L S

Jmin = |L ndash S|

Jmax = L + SJ+1J

L S

Jmin = |L ndash S|

Jmax = L + SJ+1J

VSO = A LS



А gt 0

А gt 0



J I

Fmin = |J ndash I|

Fmax = J + IF+1F

J I

Fmin = |J ndash I|

Fmax = J + IF+1F

Vhpf = AI JI


Lande interval rule






sum partpartpart

+minus=+=βα βα

αβmicroϕ

micro

2

6)0(

xxQeHWWW Q

F = J + I


H0 ψn(0) = E(0) ψn









sum=n

nn qcq )()( )0(ψψ




kmEE

kVmmVkE

m mkk ne

minus= sum )2(





H0 ψn(0) = E(0) ψn

(0) (H0 + V) ψ = E ψwhere E(0)

n = E(0)n


sum Ψ=Ψn

nn qcq )()( )0()0()0(


(0)(q)





n

( )sumprime

prime =minusn







0

21

22221

11211

=

minus

minusminus

EVVV

VEVVVVEV

NNNN

N

N

L

LLLL

L

L






J JJ

ZZZMJ EE

MJDMJMJDMJMJDMJE

γ γγγ

γγγγγγ 2EE



22


∆

plusmn=∆ γγ2E



M = ndash1

Jrsquo = 1

Jrsquorsquo = 0

M = 0

M = 1

M = 0

e perp Ze perp Z

e Z

ΔM=0

ΔM=plusmn1

σ - component

π - component

σ - component

Z E e





B me

2h


WB = - μ B


M = J J-1 hellip -J


++++minus+

+=JJ

SSLLJJg





Jrsquo = 0

M = 0

M = 1M = 0

e perp Ze perp Z

e ZΔM=0

ΔM=plusmn1

σndash - component

π - component

σ+ - component

Z Н e





dOnMJeJMmc

edW

dOnMJeJMmc

edW

ki

kab

ki

kem

ρρ

ρρ

γγπ

ω

γγπ

ω

2

23

2

2

23

2

2

)1(2

primeprimeprime=

+primeprimeprime=

minus kr

kr

pe

pe

h

h



( )sum +minus=



iii

kind

DM

ksp

DM

mce

dOIMJJMc

dW

dOMJJMc

dW

slM

M

M

22

42

2

2

2

2

3

3

h

r

h

r

h

ωρ

ρ

γmicroγπ

γmicroγπω




sum=



ii

kind

DE

ksp

DE

e

dOIMJJMc

dW

dOMJJMc

dW

rD

De

De

ωρ

ρ

γγπ

γγπω

2

2

2

2

3

3

42

h

h

Selection rules


minus harr minus )

Selection rules



Amn= 1 τ



Hydrogen Atom

reZ

mH e

e 0

22

2


h

2

2

2

2

2

22

zyxe partpart

+partpart

+partpart

=nabla ( )φθ 1 222

2 Λ+

partpart

partpart

=nablar

rrre

( )θ

θθθθθ

φθpartpart

partpart

+partpart

=Λ sinsin

1sin

1 2

2

22

Hamiltonian

Wavefunctions

-

+




Polar coordinates

kkk EH ψψ =


230

10

02aeR

ar

minus

=

230

2

020 22

2 0

a

ear

R

ar

minus

minus

= 230

2

021 62

0

a

ear

R

ar

minus

=




s 0 0 1(4 π)frac12 14 π

p11

plusmn10




d222

plusmn2plusmn10





f

3333




(716 π)frac12 (5 cos3 θ - 3 cos θ)



g

44444















1

2

2




11

s = 1(4p)frac1200

Wave Functions|ml|l



l = 0 m = 0

l = 2






Nobelpreis 1965


K32124

12

0

2

0

=minus= nna

eEnl πε







j = l + s

l s

j = l ndash frac12

j = l + frac12

2

4

3

42

21

)1( h

mellnZE jj +




z-projection


z-projection


TJ

me

eB

24102792

minussdot==h

micro

sBsZ

Bs

lBlZ

Bl

msm

l


micromicro

22minus=

minus=minus=

minus=

rr

rr









Nobelpreis 1945





JS L12 +

oJ

S L12 +

- even states

- odd states

J + J ge 1

S = 1 Triplet state

L = 0 S -state

L = 2 D -state

S = 0 Singlet state

L = 1 P -state


ΔM = 0 plusmn1

M = ndash1

J = 1

J = 0

M = 0

M = 1M = 0

Z

e perp Ze perp Z

e Z

e

ΔM = ndash 1

ΔM=0

ΔM=plusmn1

ΔM = 1



L S

Jmin = |L ndash S|

Jmax = L + SJ+1J

L S

Jmin = |L ndash S|

Jmax = L + SJ+1J

VSO = A LS



А gt 0

А gt 0



J I

Fmin = |J ndash I|

Fmax = J + IF+1F

J I

Fmin = |J ndash I|

Fmax = J + IF+1F

Vhpf = AI JI


Lande interval rule






sum partpartpart

+minus=+=βα βα

αβmicroϕ

micro

2

6)0(

xxQeHWWW Q

F = J + I


H0 ψn(0) = E(0) ψn









sum=n

nn qcq )()( )0(ψψ




kmEE

kVmmVkE

m mkk ne

minus= sum )2(





H0 ψn(0) = E(0) ψn

(0) (H0 + V) ψ = E ψwhere E(0)

n = E(0)n


sum Ψ=Ψn

nn qcq )()( )0()0()0(


(0)(q)





n

( )sumprime

prime =minusn







0

21

22221

11211

=

minus

minusminus

EVVV

VEVVVVEV

NNNN

N

N

L

LLLL

L

L






J JJ

ZZZMJ EE

MJDMJMJDMJMJDMJE

γ γγγ

γγγγγγ 2EE



22


∆

plusmn=∆ γγ2E



M = ndash1

Jrsquo = 1

Jrsquorsquo = 0

M = 0

M = 1

M = 0

e perp Ze perp Z

e Z

ΔM=0

ΔM=plusmn1

σ - component

π - component

σ - component

Z E e





B me

2h


WB = - μ B


M = J J-1 hellip -J


++++minus+

+=JJ

SSLLJJg





Jrsquo = 0

M = 0

M = 1M = 0

e perp Ze perp Z

e ZΔM=0

ΔM=plusmn1

σndash - component

π - component

σ+ - component

Z Н e





dOnMJeJMmc

edW

dOnMJeJMmc

edW

ki

kab

ki

kem

ρρ

ρρ

γγπ

ω

γγπ

ω

2

23

2

2

23

2

2

)1(2

primeprimeprime=

+primeprimeprime=

minus kr

kr

pe

pe

h

h



( )sum +minus=



iii

kind

DM

ksp

DM

mce

dOIMJJMc

dW

dOMJJMc

dW

slM

M

M

22

42

2

2

2

2

3

3

h

r

h

r

h

ωρ

ρ

γmicroγπ

γmicroγπω




sum=



ii

kind

DE

ksp

DE

e

dOIMJJMc

dW

dOMJJMc

dW

rD

De

De

ωρ

ρ

γγπ

γγπω

2

2

2

2

3

3

42

h

h

Selection rules


minus harr minus )

Selection rules



Amn= 1 τ




230

10

02aeR

ar

minus

=

230

2

020 22

2 0

a

ear

R

ar

minus

minus

= 230

2

021 62

0

a

ear

R

ar

minus

=




s 0 0 1(4 π)frac12 14 π

p11

plusmn10




d222

plusmn2plusmn10





f

3333




(716 π)frac12 (5 cos3 θ - 3 cos θ)



g

44444















1

2

2




11

s = 1(4p)frac1200

Wave Functions|ml|l



l = 0 m = 0

l = 2






Nobelpreis 1965


K32124

12

0

2

0

=minus= nna

eEnl πε







j = l + s

l s

j = l ndash frac12

j = l + frac12

2

4

3

42

21

)1( h

mellnZE jj +




z-projection


z-projection


TJ

me

eB

24102792

minussdot==h

micro

sBsZ

Bs

lBlZ

Bl

msm

l


micromicro

22minus=

minus=minus=

minus=

rr

rr









Nobelpreis 1945





JS L12 +

oJ

S L12 +

- even states

- odd states

J + J ge 1

S = 1 Triplet state

L = 0 S -state

L = 2 D -state

S = 0 Singlet state

L = 1 P -state


ΔM = 0 plusmn1

M = ndash1

J = 1

J = 0

M = 0

M = 1M = 0

Z

e perp Ze perp Z

e Z

e

ΔM = ndash 1

ΔM=0

ΔM=plusmn1

ΔM = 1



L S

Jmin = |L ndash S|

Jmax = L + SJ+1J

L S

Jmin = |L ndash S|

Jmax = L + SJ+1J

VSO = A LS



А gt 0

А gt 0



J I

Fmin = |J ndash I|

Fmax = J + IF+1F

J I

Fmin = |J ndash I|

Fmax = J + IF+1F

Vhpf = AI JI


Lande interval rule






sum partpartpart

+minus=+=βα βα

αβmicroϕ

micro

2

6)0(

xxQeHWWW Q

F = J + I


H0 ψn(0) = E(0) ψn









sum=n

nn qcq )()( )0(ψψ




kmEE

kVmmVkE

m mkk ne

minus= sum )2(





H0 ψn(0) = E(0) ψn

(0) (H0 + V) ψ = E ψwhere E(0)

n = E(0)n


sum Ψ=Ψn

nn qcq )()( )0()0()0(


(0)(q)





n

( )sumprime

prime =minusn







0

21

22221

11211

=

minus

minusminus

EVVV

VEVVVVEV

NNNN

N

N

L

LLLL

L

L






J JJ

ZZZMJ EE

MJDMJMJDMJMJDMJE

γ γγγ

γγγγγγ 2EE



22


∆

plusmn=∆ γγ2E



M = ndash1

Jrsquo = 1

Jrsquorsquo = 0

M = 0

M = 1

M = 0

e perp Ze perp Z

e Z

ΔM=0

ΔM=plusmn1

σ - component

π - component

σ - component

Z E e





B me

2h


WB = - μ B


M = J J-1 hellip -J


++++minus+

+=JJ

SSLLJJg





Jrsquo = 0

M = 0

M = 1M = 0

e perp Ze perp Z

e ZΔM=0

ΔM=plusmn1

σndash - component

π - component

σ+ - component

Z Н e





dOnMJeJMmc

edW

dOnMJeJMmc

edW

ki

kab

ki

kem

ρρ

ρρ

γγπ

ω

γγπ

ω

2

23

2

2

23

2

2

)1(2

primeprimeprime=

+primeprimeprime=

minus kr

kr

pe

pe

h

h



( )sum +minus=



iii

kind

DM

ksp

DM

mce

dOIMJJMc

dW

dOMJJMc

dW

slM

M

M

22

42

2

2

2

2

3

3

h

r

h

r

h

ωρ

ρ

γmicroγπ

γmicroγπω




sum=



ii

kind

DE

ksp

DE

e

dOIMJJMc

dW

dOMJJMc

dW

rD

De

De

ωρ

ρ

γγπ

γγπω

2

2

2

2

3

3

42

h

h

Selection rules


minus harr minus )

Selection rules



Amn= 1 τ






s 0 0 1(4 π)frac12 14 π

p11

plusmn10




d222

plusmn2plusmn10





f

3333




(716 π)frac12 (5 cos3 θ - 3 cos θ)



g

44444















1

2

2




11

s = 1(4p)frac1200

Wave Functions|ml|l



l = 0 m = 0

l = 2






Nobelpreis 1965


K32124

12

0

2

0

=minus= nna

eEnl πε







j = l + s

l s

j = l ndash frac12

j = l + frac12

2

4

3

42

21

)1( h

mellnZE jj +




z-projection


z-projection


TJ

me

eB

24102792

minussdot==h

micro

sBsZ

Bs

lBlZ

Bl

msm

l


micromicro

22minus=

minus=minus=

minus=

rr

rr









Nobelpreis 1945





JS L12 +

oJ

S L12 +

- even states

- odd states

J + J ge 1

S = 1 Triplet state

L = 0 S -state

L = 2 D -state

S = 0 Singlet state

L = 1 P -state


ΔM = 0 plusmn1

M = ndash1

J = 1

J = 0

M = 0

M = 1M = 0

Z

e perp Ze perp Z

e Z

e

ΔM = ndash 1

ΔM=0

ΔM=plusmn1

ΔM = 1



L S

Jmin = |L ndash S|

Jmax = L + SJ+1J

L S

Jmin = |L ndash S|

Jmax = L + SJ+1J

VSO = A LS



А gt 0

А gt 0



J I

Fmin = |J ndash I|

Fmax = J + IF+1F

J I

Fmin = |J ndash I|

Fmax = J + IF+1F

Vhpf = AI JI


Lande interval rule






sum partpartpart

+minus=+=βα βα

αβmicroϕ

micro

2

6)0(

xxQeHWWW Q

F = J + I


H0 ψn(0) = E(0) ψn









sum=n

nn qcq )()( )0(ψψ




kmEE

kVmmVkE

m mkk ne

minus= sum )2(





H0 ψn(0) = E(0) ψn

(0) (H0 + V) ψ = E ψwhere E(0)

n = E(0)n


sum Ψ=Ψn

nn qcq )()( )0()0()0(


(0)(q)





n

( )sumprime

prime =minusn







0

21

22221

11211

=

minus

minusminus

EVVV

VEVVVVEV

NNNN

N

N

L

LLLL

L

L






J JJ

ZZZMJ EE

MJDMJMJDMJMJDMJE

γ γγγ

γγγγγγ 2EE



22


∆

plusmn=∆ γγ2E



M = ndash1

Jrsquo = 1

Jrsquorsquo = 0

M = 0

M = 1

M = 0

e perp Ze perp Z

e Z

ΔM=0

ΔM=plusmn1

σ - component

π - component

σ - component

Z E e





B me

2h


WB = - μ B


M = J J-1 hellip -J


++++minus+

+=JJ

SSLLJJg





Jrsquo = 0

M = 0

M = 1M = 0

e perp Ze perp Z

e ZΔM=0

ΔM=plusmn1

σndash - component

π - component

σ+ - component

Z Н e





dOnMJeJMmc

edW

dOnMJeJMmc

edW

ki

kab

ki

kem

ρρ

ρρ

γγπ

ω

γγπ

ω

2

23

2

2

23

2

2

)1(2

primeprimeprime=

+primeprimeprime=

minus kr

kr

pe

pe

h

h



( )sum +minus=



iii

kind

DM

ksp

DM

mce

dOIMJJMc

dW

dOMJJMc

dW

slM

M

M

22

42

2

2

2

2

3

3

h

r

h

r

h

ωρ

ρ

γmicroγπ

γmicroγπω




sum=



ii

kind

DE

ksp

DE

e

dOIMJJMc

dW

dOMJJMc

dW

rD

De

De

ωρ

ρ

γγπ

γγπω

2

2

2

2

3

3

42

h

h

Selection rules


minus harr minus )

Selection rules



Amn= 1 τ









1

2

2




11

s = 1(4p)frac1200

Wave Functions|ml|l



l = 0 m = 0

l = 2






Nobelpreis 1965


K32124

12

0

2

0

=minus= nna

eEnl πε







j = l + s

l s

j = l ndash frac12

j = l + frac12

2

4

3

42

21

)1( h

mellnZE jj +




z-projection


z-projection


TJ

me

eB

24102792

minussdot==h

micro

sBsZ

Bs

lBlZ

Bl

msm

l


micromicro

22minus=

minus=minus=

minus=

rr

rr









Nobelpreis 1945





JS L12 +

oJ

S L12 +

- even states

- odd states

J + J ge 1

S = 1 Triplet state

L = 0 S -state

L = 2 D -state

S = 0 Singlet state

L = 1 P -state


ΔM = 0 plusmn1

M = ndash1

J = 1

J = 0

M = 0

M = 1M = 0

Z

e perp Ze perp Z

e Z

e

ΔM = ndash 1

ΔM=0

ΔM=plusmn1

ΔM = 1



L S

Jmin = |L ndash S|

Jmax = L + SJ+1J

L S

Jmin = |L ndash S|

Jmax = L + SJ+1J

VSO = A LS



А gt 0

А gt 0



J I

Fmin = |J ndash I|

Fmax = J + IF+1F

J I

Fmin = |J ndash I|

Fmax = J + IF+1F

Vhpf = AI JI


Lande interval rule






sum partpartpart

+minus=+=βα βα

αβmicroϕ

micro

2

6)0(

xxQeHWWW Q

F = J + I


H0 ψn(0) = E(0) ψn









sum=n

nn qcq )()( )0(ψψ




kmEE

kVmmVkE

m mkk ne

minus= sum )2(





H0 ψn(0) = E(0) ψn

(0) (H0 + V) ψ = E ψwhere E(0)

n = E(0)n


sum Ψ=Ψn

nn qcq )()( )0()0()0(


(0)(q)





n

( )sumprime

prime =minusn







0

21

22221

11211

=

minus

minusminus

EVVV

VEVVVVEV

NNNN

N

N

L

LLLL

L

L






J JJ

ZZZMJ EE

MJDMJMJDMJMJDMJE

γ γγγ

γγγγγγ 2EE



22


∆

plusmn=∆ γγ2E



M = ndash1

Jrsquo = 1

Jrsquorsquo = 0

M = 0

M = 1

M = 0

e perp Ze perp Z

e Z

ΔM=0

ΔM=plusmn1

σ - component

π - component

σ - component

Z E e





B me

2h


WB = - μ B


M = J J-1 hellip -J


++++minus+

+=JJ

SSLLJJg





Jrsquo = 0

M = 0

M = 1M = 0

e perp Ze perp Z

e ZΔM=0

ΔM=plusmn1

σndash - component

π - component

σ+ - component

Z Н e





dOnMJeJMmc

edW

dOnMJeJMmc

edW

ki

kab

ki

kem

ρρ

ρρ

γγπ

ω

γγπ

ω

2

23

2

2

23

2

2

)1(2

primeprimeprime=

+primeprimeprime=

minus kr

kr

pe

pe

h

h



( )sum +minus=



iii

kind

DM

ksp

DM

mce

dOIMJJMc

dW

dOMJJMc

dW

slM

M

M

22

42

2

2

2

2

3

3

h

r

h

r

h

ωρ

ρ

γmicroγπ

γmicroγπω




sum=



ii

kind

DE

ksp

DE

e

dOIMJJMc

dW

dOMJJMc

dW

rD

De

De

ωρ

ρ

γγπ

γγπω

2

2

2

2

3

3

42

h

h

Selection rules


minus harr minus )

Selection rules



Amn= 1 τ





l = 0 m = 0

l = 2






Nobelpreis 1965


K32124

12

0

2

0

=minus= nna

eEnl πε







j = l + s

l s

j = l ndash frac12

j = l + frac12

2

4

3

42

21

)1( h

mellnZE jj +




z-projection


z-projection


TJ

me

eB

24102792

minussdot==h

micro

sBsZ

Bs

lBlZ

Bl

msm

l


micromicro

22minus=

minus=minus=

minus=

rr

rr









Nobelpreis 1945





JS L12 +

oJ

S L12 +

- even states

- odd states

J + J ge 1

S = 1 Triplet state

L = 0 S -state

L = 2 D -state

S = 0 Singlet state

L = 1 P -state


ΔM = 0 plusmn1

M = ndash1

J = 1

J = 0

M = 0

M = 1M = 0

Z

e perp Ze perp Z

e Z

e

ΔM = ndash 1

ΔM=0

ΔM=plusmn1

ΔM = 1



L S

Jmin = |L ndash S|

Jmax = L + SJ+1J

L S

Jmin = |L ndash S|

Jmax = L + SJ+1J

VSO = A LS



А gt 0

А gt 0



J I

Fmin = |J ndash I|

Fmax = J + IF+1F

J I

Fmin = |J ndash I|

Fmax = J + IF+1F

Vhpf = AI JI


Lande interval rule






sum partpartpart

+minus=+=βα βα

αβmicroϕ

micro

2

6)0(

xxQeHWWW Q

F = J + I


H0 ψn(0) = E(0) ψn









sum=n

nn qcq )()( )0(ψψ




kmEE

kVmmVkE

m mkk ne

minus= sum )2(





H0 ψn(0) = E(0) ψn

(0) (H0 + V) ψ = E ψwhere E(0)

n = E(0)n


sum Ψ=Ψn

nn qcq )()( )0()0()0(


(0)(q)





n

( )sumprime

prime =minusn







0

21

22221

11211

=

minus

minusminus

EVVV

VEVVVVEV

NNNN

N

N

L

LLLL

L

L






J JJ

ZZZMJ EE

MJDMJMJDMJMJDMJE

γ γγγ

γγγγγγ 2EE



22


∆

plusmn=∆ γγ2E



M = ndash1

Jrsquo = 1

Jrsquorsquo = 0

M = 0

M = 1

M = 0

e perp Ze perp Z

e Z

ΔM=0

ΔM=plusmn1

σ - component

π - component

σ - component

Z E e





B me

2h


WB = - μ B


M = J J-1 hellip -J


++++minus+

+=JJ

SSLLJJg





Jrsquo = 0

M = 0

M = 1M = 0

e perp Ze perp Z

e ZΔM=0

ΔM=plusmn1

σndash - component

π - component

σ+ - component

Z Н e





dOnMJeJMmc

edW

dOnMJeJMmc

edW

ki

kab

ki

kem

ρρ

ρρ

γγπ

ω

γγπ

ω

2

23

2

2

23

2

2

)1(2

primeprimeprime=

+primeprimeprime=

minus kr

kr

pe

pe

h

h



( )sum +minus=



iii

kind

DM

ksp

DM

mce

dOIMJJMc

dW

dOMJJMc

dW

slM

M

M

22

42

2

2

2

2

3

3

h

r

h

r

h

ωρ

ρ

γmicroγπ

γmicroγπω




sum=



ii

kind

DE

ksp

DE

e

dOIMJJMc

dW

dOMJJMc

dW

rD

De

De

ωρ

ρ

γγπ

γγπω

2

2

2

2

3

3

42

h

h

Selection rules


minus harr minus )

Selection rules



Amn= 1 τ





Nobelpreis 1965


K32124

12

0

2

0

=minus= nna

eEnl πε







j = l + s

l s

j = l ndash frac12

j = l + frac12

2

4

3

42

21

)1( h

mellnZE jj +




z-projection


z-projection


TJ

me

eB

24102792

minussdot==h

micro

sBsZ

Bs

lBlZ

Bl

msm

l


micromicro

22minus=

minus=minus=

minus=

rr

rr









Nobelpreis 1945





JS L12 +

oJ

S L12 +

- even states

- odd states

J + J ge 1

S = 1 Triplet state

L = 0 S -state

L = 2 D -state

S = 0 Singlet state

L = 1 P -state


ΔM = 0 plusmn1

M = ndash1

J = 1

J = 0

M = 0

M = 1M = 0

Z

e perp Ze perp Z

e Z

e

ΔM = ndash 1

ΔM=0

ΔM=plusmn1

ΔM = 1



L S

Jmin = |L ndash S|

Jmax = L + SJ+1J

L S

Jmin = |L ndash S|

Jmax = L + SJ+1J

VSO = A LS



А gt 0

А gt 0



J I

Fmin = |J ndash I|

Fmax = J + IF+1F

J I

Fmin = |J ndash I|

Fmax = J + IF+1F

Vhpf = AI JI


Lande interval rule






sum partpartpart

+minus=+=βα βα

αβmicroϕ

micro

2

6)0(

xxQeHWWW Q

F = J + I


H0 ψn(0) = E(0) ψn









sum=n

nn qcq )()( )0(ψψ




kmEE

kVmmVkE

m mkk ne

minus= sum )2(





H0 ψn(0) = E(0) ψn

(0) (H0 + V) ψ = E ψwhere E(0)

n = E(0)n


sum Ψ=Ψn

nn qcq )()( )0()0()0(


(0)(q)





n

( )sumprime

prime =minusn







0

21

22221

11211

=

minus

minusminus

EVVV

VEVVVVEV

NNNN

N

N

L

LLLL

L

L






J JJ

ZZZMJ EE

MJDMJMJDMJMJDMJE

γ γγγ

γγγγγγ 2EE



22


∆

plusmn=∆ γγ2E



M = ndash1

Jrsquo = 1

Jrsquorsquo = 0

M = 0

M = 1

M = 0

e perp Ze perp Z

e Z

ΔM=0

ΔM=plusmn1

σ - component

π - component

σ - component

Z E e





B me

2h


WB = - μ B


M = J J-1 hellip -J


++++minus+

+=JJ

SSLLJJg





Jrsquo = 0

M = 0

M = 1M = 0

e perp Ze perp Z

e ZΔM=0

ΔM=plusmn1

σndash - component

π - component

σ+ - component

Z Н e





dOnMJeJMmc

edW

dOnMJeJMmc

edW

ki

kab

ki

kem

ρρ

ρρ

γγπ

ω

γγπ

ω

2

23

2

2

23

2

2

)1(2

primeprimeprime=

+primeprimeprime=

minus kr

kr

pe

pe

h

h



( )sum +minus=



iii

kind

DM

ksp

DM

mce

dOIMJJMc

dW

dOMJJMc

dW

slM

M

M

22

42

2

2

2

2

3

3

h

r

h

r

h

ωρ

ρ

γmicroγπ

γmicroγπω




sum=



ii

kind

DE

ksp

DE

e

dOIMJJMc

dW

dOMJJMc

dW

rD

De

De

ωρ

ρ

γγπ

γγπω

2

2

2

2

3

3

42

h

h

Selection rules


minus harr minus )

Selection rules



Amn= 1 τ




K32124

12

0

2

0

=minus= nna

eEnl πε







j = l + s

l s

j = l ndash frac12

j = l + frac12

2

4

3

42

21

)1( h

mellnZE jj +




z-projection


z-projection


TJ

me

eB

24102792

minussdot==h

micro

sBsZ

Bs

lBlZ

Bl

msm

l


micromicro

22minus=

minus=minus=

minus=

rr

rr









Nobelpreis 1945





JS L12 +

oJ

S L12 +

- even states

- odd states

J + J ge 1

S = 1 Triplet state

L = 0 S -state

L = 2 D -state

S = 0 Singlet state

L = 1 P -state


ΔM = 0 plusmn1

M = ndash1

J = 1

J = 0

M = 0

M = 1M = 0

Z

e perp Ze perp Z

e Z

e

ΔM = ndash 1

ΔM=0

ΔM=plusmn1

ΔM = 1



L S

Jmin = |L ndash S|

Jmax = L + SJ+1J

L S

Jmin = |L ndash S|

Jmax = L + SJ+1J

VSO = A LS



А gt 0

А gt 0



J I

Fmin = |J ndash I|

Fmax = J + IF+1F

J I

Fmin = |J ndash I|

Fmax = J + IF+1F

Vhpf = AI JI


Lande interval rule






sum partpartpart

+minus=+=βα βα

αβmicroϕ

micro

2

6)0(

xxQeHWWW Q

F = J + I


H0 ψn(0) = E(0) ψn









sum=n

nn qcq )()( )0(ψψ




kmEE

kVmmVkE

m mkk ne

minus= sum )2(





H0 ψn(0) = E(0) ψn

(0) (H0 + V) ψ = E ψwhere E(0)

n = E(0)n


sum Ψ=Ψn

nn qcq )()( )0()0()0(


(0)(q)





n

( )sumprime

prime =minusn







0

21

22221

11211

=

minus

minusminus

EVVV

VEVVVVEV

NNNN

N

N

L

LLLL

L

L






J JJ

ZZZMJ EE

MJDMJMJDMJMJDMJE

γ γγγ

γγγγγγ 2EE



22


∆

plusmn=∆ γγ2E



M = ndash1

Jrsquo = 1

Jrsquorsquo = 0

M = 0

M = 1

M = 0

e perp Ze perp Z

e Z

ΔM=0

ΔM=plusmn1

σ - component

π - component

σ - component

Z E e





B me

2h


WB = - μ B


M = J J-1 hellip -J


++++minus+

+=JJ

SSLLJJg





Jrsquo = 0

M = 0

M = 1M = 0

e perp Ze perp Z

e ZΔM=0

ΔM=plusmn1

σndash - component

π - component

σ+ - component

Z Н e





dOnMJeJMmc

edW

dOnMJeJMmc

edW

ki

kab

ki

kem

ρρ

ρρ

γγπ

ω

γγπ

ω

2

23

2

2

23

2

2

)1(2

primeprimeprime=

+primeprimeprime=

minus kr

kr

pe

pe

h

h



( )sum +minus=



iii

kind

DM

ksp

DM

mce

dOIMJJMc

dW

dOMJJMc

dW

slM

M

M

22

42

2

2

2

2

3

3

h

r

h

r

h

ωρ

ρ

γmicroγπ

γmicroγπω




sum=



ii

kind

DE

ksp

DE

e

dOIMJJMc

dW

dOMJJMc

dW

rD

De

De

ωρ

ρ

γγπ

γγπω

2

2

2

2

3

3

42

h

h

Selection rules


minus harr minus )

Selection rules



Amn= 1 τ





j = l + s

l s

j = l ndash frac12

j = l + frac12

2

4

3

42

21

)1( h

mellnZE jj +




z-projection


z-projection


TJ

me

eB

24102792

minussdot==h

micro

sBsZ

Bs

lBlZ

Bl

msm

l


micromicro

22minus=

minus=minus=

minus=

rr

rr









Nobelpreis 1945





JS L12 +

oJ

S L12 +

- even states

- odd states

J + J ge 1

S = 1 Triplet state

L = 0 S -state

L = 2 D -state

S = 0 Singlet state

L = 1 P -state


ΔM = 0 plusmn1

M = ndash1

J = 1

J = 0

M = 0

M = 1M = 0

Z

e perp Ze perp Z

e Z

e

ΔM = ndash 1

ΔM=0

ΔM=plusmn1

ΔM = 1



L S

Jmin = |L ndash S|

Jmax = L + SJ+1J

L S

Jmin = |L ndash S|

Jmax = L + SJ+1J

VSO = A LS



А gt 0

А gt 0



J I

Fmin = |J ndash I|

Fmax = J + IF+1F

J I

Fmin = |J ndash I|

Fmax = J + IF+1F

Vhpf = AI JI


Lande interval rule






sum partpartpart

+minus=+=βα βα

αβmicroϕ

micro

2

6)0(

xxQeHWWW Q

F = J + I


H0 ψn(0) = E(0) ψn









sum=n

nn qcq )()( )0(ψψ




kmEE

kVmmVkE

m mkk ne

minus= sum )2(





H0 ψn(0) = E(0) ψn

(0) (H0 + V) ψ = E ψwhere E(0)

n = E(0)n


sum Ψ=Ψn

nn qcq )()( )0()0()0(


(0)(q)





n

( )sumprime

prime =minusn







0

21

22221

11211

=

minus

minusminus

EVVV

VEVVVVEV

NNNN

N

N

L

LLLL

L

L






J JJ

ZZZMJ EE

MJDMJMJDMJMJDMJE

γ γγγ

γγγγγγ 2EE



22


∆

plusmn=∆ γγ2E



M = ndash1

Jrsquo = 1

Jrsquorsquo = 0

M = 0

M = 1

M = 0

e perp Ze perp Z

e Z

ΔM=0

ΔM=plusmn1

σ - component

π - component

σ - component

Z E e





B me

2h


WB = - μ B


M = J J-1 hellip -J


++++minus+

+=JJ

SSLLJJg





Jrsquo = 0

M = 0

M = 1M = 0

e perp Ze perp Z

e ZΔM=0

ΔM=plusmn1

σndash - component

π - component

σ+ - component

Z Н e





dOnMJeJMmc

edW

dOnMJeJMmc

edW

ki

kab

ki

kem

ρρ

ρρ

γγπ

ω

γγπ

ω

2

23

2

2

23

2

2

)1(2

primeprimeprime=

+primeprimeprime=

minus kr

kr

pe

pe

h

h



( )sum +minus=



iii

kind

DM

ksp

DM

mce

dOIMJJMc

dW

dOMJJMc

dW

slM

M

M

22

42

2

2

2

2

3

3

h

r

h

r

h

ωρ

ρ

γmicroγπ

γmicroγπω




sum=



ii

kind

DE

ksp

DE

e

dOIMJJMc

dW

dOMJJMc

dW

rD

De

De

ωρ

ρ

γγπ

γγπω

2

2

2

2

3

3

42

h

h

Selection rules


minus harr minus )

Selection rules



Amn= 1 τ











Nobelpreis 1945





JS L12 +

oJ

S L12 +

- even states

- odd states

J + J ge 1

S = 1 Triplet state

L = 0 S -state

L = 2 D -state

S = 0 Singlet state

L = 1 P -state


ΔM = 0 plusmn1

M = ndash1

J = 1

J = 0

M = 0

M = 1M = 0

Z

e perp Ze perp Z

e Z

e

ΔM = ndash 1

ΔM=0

ΔM=plusmn1

ΔM = 1



L S

Jmin = |L ndash S|

Jmax = L + SJ+1J

L S

Jmin = |L ndash S|

Jmax = L + SJ+1J

VSO = A LS



А gt 0

А gt 0



J I

Fmin = |J ndash I|

Fmax = J + IF+1F

J I

Fmin = |J ndash I|

Fmax = J + IF+1F

Vhpf = AI JI


Lande interval rule






sum partpartpart

+minus=+=βα βα

αβmicroϕ

micro

2

6)0(

xxQeHWWW Q

F = J + I


H0 ψn(0) = E(0) ψn









sum=n

nn qcq )()( )0(ψψ




kmEE

kVmmVkE

m mkk ne

minus= sum )2(





H0 ψn(0) = E(0) ψn

(0) (H0 + V) ψ = E ψwhere E(0)

n = E(0)n


sum Ψ=Ψn

nn qcq )()( )0()0()0(


(0)(q)





n

( )sumprime

prime =minusn







0

21

22221

11211

=

minus

minusminus

EVVV

VEVVVVEV

NNNN

N

N

L

LLLL

L

L






J JJ

ZZZMJ EE

MJDMJMJDMJMJDMJE

γ γγγ

γγγγγγ 2EE



22


∆

plusmn=∆ γγ2E



M = ndash1

Jrsquo = 1

Jrsquorsquo = 0

M = 0

M = 1

M = 0

e perp Ze perp Z

e Z

ΔM=0

ΔM=plusmn1

σ - component

π - component

σ - component

Z E e





B me

2h


WB = - μ B


M = J J-1 hellip -J


++++minus+

+=JJ

SSLLJJg





Jrsquo = 0

M = 0

M = 1M = 0

e perp Ze perp Z

e ZΔM=0

ΔM=plusmn1

σndash - component

π - component

σ+ - component

Z Н e





dOnMJeJMmc

edW

dOnMJeJMmc

edW

ki

kab

ki

kem

ρρ

ρρ

γγπ

ω

γγπ

ω

2

23

2

2

23

2

2

)1(2

primeprimeprime=

+primeprimeprime=

minus kr

kr

pe

pe

h

h



( )sum +minus=



iii

kind

DM

ksp

DM

mce

dOIMJJMc

dW

dOMJJMc

dW

slM

M

M

22

42

2

2

2

2

3

3

h

r

h

r

h

ωρ

ρ

γmicroγπ

γmicroγπω




sum=



ii

kind

DE

ksp

DE

e

dOIMJJMc

dW

dOMJJMc

dW

rD

De

De

ωρ

ρ

γγπ

γγπω

2

2

2

2

3

3

42

h

h

Selection rules


minus harr minus )

Selection rules



Amn= 1 τ







JS L12 +

oJ

S L12 +

- even states

- odd states

J + J ge 1

S = 1 Triplet state

L = 0 S -state

L = 2 D -state

S = 0 Singlet state

L = 1 P -state


ΔM = 0 plusmn1

M = ndash1

J = 1

J = 0

M = 0

M = 1M = 0

Z

e perp Ze perp Z

e Z

e

ΔM = ndash 1

ΔM=0

ΔM=plusmn1

ΔM = 1



L S

Jmin = |L ndash S|

Jmax = L + SJ+1J

L S

Jmin = |L ndash S|

Jmax = L + SJ+1J

VSO = A LS



А gt 0

А gt 0



J I

Fmin = |J ndash I|

Fmax = J + IF+1F

J I

Fmin = |J ndash I|

Fmax = J + IF+1F

Vhpf = AI JI


Lande interval rule






sum partpartpart

+minus=+=βα βα

αβmicroϕ

micro

2

6)0(

xxQeHWWW Q

F = J + I


H0 ψn(0) = E(0) ψn









sum=n

nn qcq )()( )0(ψψ




kmEE

kVmmVkE

m mkk ne

minus= sum )2(





H0 ψn(0) = E(0) ψn

(0) (H0 + V) ψ = E ψwhere E(0)

n = E(0)n


sum Ψ=Ψn

nn qcq )()( )0()0()0(


(0)(q)





n

( )sumprime

prime =minusn







0

21

22221

11211

=

minus

minusminus

EVVV

VEVVVVEV

NNNN

N

N

L

LLLL

L

L






J JJ

ZZZMJ EE

MJDMJMJDMJMJDMJE

γ γγγ

γγγγγγ 2EE



22


∆

plusmn=∆ γγ2E



M = ndash1

Jrsquo = 1

Jrsquorsquo = 0

M = 0

M = 1

M = 0

e perp Ze perp Z

e Z

ΔM=0

ΔM=plusmn1

σ - component

π - component

σ - component

Z E e





B me

2h


WB = - μ B


M = J J-1 hellip -J


++++minus+

+=JJ

SSLLJJg





Jrsquo = 0

M = 0

M = 1M = 0

e perp Ze perp Z

e ZΔM=0

ΔM=plusmn1

σndash - component

π - component

σ+ - component

Z Н e





dOnMJeJMmc

edW

dOnMJeJMmc

edW

ki

kab

ki

kem

ρρ

ρρ

γγπ

ω

γγπ

ω

2

23

2

2

23

2

2

)1(2

primeprimeprime=

+primeprimeprime=

minus kr

kr

pe

pe

h

h



( )sum +minus=



iii

kind

DM

ksp

DM

mce

dOIMJJMc

dW

dOMJJMc

dW

slM

M

M

22

42

2

2

2

2

3

3

h

r

h

r

h

ωρ

ρ

γmicroγπ

γmicroγπω




sum=



ii

kind

DE

ksp

DE

e

dOIMJJMc

dW

dOMJJMc

dW

rD

De

De

ωρ

ρ

γγπ

γγπω

2

2

2

2

3

3

42

h

h

Selection rules


minus harr minus )

Selection rules



Amn= 1 τ




ΔM = 0 plusmn1

M = ndash1

J = 1

J = 0

M = 0

M = 1M = 0

Z

e perp Ze perp Z

e Z

e

ΔM = ndash 1

ΔM=0

ΔM=plusmn1

ΔM = 1



L S

Jmin = |L ndash S|

Jmax = L + SJ+1J

L S

Jmin = |L ndash S|

Jmax = L + SJ+1J

VSO = A LS



А gt 0

А gt 0



J I

Fmin = |J ndash I|

Fmax = J + IF+1F

J I

Fmin = |J ndash I|

Fmax = J + IF+1F

Vhpf = AI JI


Lande interval rule






sum partpartpart

+minus=+=βα βα

αβmicroϕ

micro

2

6)0(

xxQeHWWW Q

F = J + I


H0 ψn(0) = E(0) ψn









sum=n

nn qcq )()( )0(ψψ




kmEE

kVmmVkE

m mkk ne

minus= sum )2(





H0 ψn(0) = E(0) ψn

(0) (H0 + V) ψ = E ψwhere E(0)

n = E(0)n


sum Ψ=Ψn

nn qcq )()( )0()0()0(


(0)(q)





n

( )sumprime

prime =minusn







0

21

22221

11211

=

minus

minusminus

EVVV

VEVVVVEV

NNNN

N

N

L

LLLL

L

L






J JJ

ZZZMJ EE

MJDMJMJDMJMJDMJE

γ γγγ

γγγγγγ 2EE



22


∆

plusmn=∆ γγ2E



M = ndash1

Jrsquo = 1

Jrsquorsquo = 0

M = 0

M = 1

M = 0

e perp Ze perp Z

e Z

ΔM=0

ΔM=plusmn1

σ - component

π - component

σ - component

Z E e





B me

2h


WB = - μ B


M = J J-1 hellip -J


++++minus+

+=JJ

SSLLJJg





Jrsquo = 0

M = 0

M = 1M = 0

e perp Ze perp Z

e ZΔM=0

ΔM=plusmn1

σndash - component

π - component

σ+ - component

Z Н e





dOnMJeJMmc

edW

dOnMJeJMmc

edW

ki

kab

ki

kem

ρρ

ρρ

γγπ

ω

γγπ

ω

2

23

2

2

23

2

2

)1(2

primeprimeprime=

+primeprimeprime=

minus kr

kr

pe

pe

h

h



( )sum +minus=



iii

kind

DM

ksp

DM

mce

dOIMJJMc

dW

dOMJJMc

dW

slM

M

M

22

42

2

2

2

2

3

3

h

r

h

r

h

ωρ

ρ

γmicroγπ

γmicroγπω




sum=



ii

kind

DE

ksp

DE

e

dOIMJJMc

dW

dOMJJMc

dW

rD

De

De

ωρ

ρ

γγπ

γγπω

2

2

2

2

3

3

42

h

h

Selection rules


minus harr minus )

Selection rules



Amn= 1 τ




L S

Jmin = |L ndash S|

Jmax = L + SJ+1J

L S

Jmin = |L ndash S|

Jmax = L + SJ+1J

VSO = A LS



А gt 0

А gt 0



J I

Fmin = |J ndash I|

Fmax = J + IF+1F

J I

Fmin = |J ndash I|

Fmax = J + IF+1F

Vhpf = AI JI


Lande interval rule






sum partpartpart

+minus=+=βα βα

αβmicroϕ

micro

2

6)0(

xxQeHWWW Q

F = J + I


H0 ψn(0) = E(0) ψn









sum=n

nn qcq )()( )0(ψψ




kmEE

kVmmVkE

m mkk ne

minus= sum )2(





H0 ψn(0) = E(0) ψn

(0) (H0 + V) ψ = E ψwhere E(0)

n = E(0)n


sum Ψ=Ψn

nn qcq )()( )0()0()0(


(0)(q)





n

( )sumprime

prime =minusn







0

21

22221

11211

=

minus

minusminus

EVVV

VEVVVVEV

NNNN

N

N

L

LLLL

L

L






J JJ

ZZZMJ EE

MJDMJMJDMJMJDMJE

γ γγγ

γγγγγγ 2EE



22


∆

plusmn=∆ γγ2E



M = ndash1

Jrsquo = 1

Jrsquorsquo = 0

M = 0

M = 1

M = 0

e perp Ze perp Z

e Z

ΔM=0

ΔM=plusmn1

σ - component

π - component

σ - component

Z E e





B me

2h


WB = - μ B


M = J J-1 hellip -J


++++minus+

+=JJ

SSLLJJg





Jrsquo = 0

M = 0

M = 1M = 0

e perp Ze perp Z

e ZΔM=0

ΔM=plusmn1

σndash - component

π - component

σ+ - component

Z Н e





dOnMJeJMmc

edW

dOnMJeJMmc

edW

ki

kab

ki

kem

ρρ

ρρ

γγπ

ω

γγπ

ω

2

23

2

2

23

2

2

)1(2

primeprimeprime=

+primeprimeprime=

minus kr

kr

pe

pe

h

h



( )sum +minus=



iii

kind

DM

ksp

DM

mce

dOIMJJMc

dW

dOMJJMc

dW

slM

M

M

22

42

2

2

2

2

3

3

h

r

h

r

h

ωρ

ρ

γmicroγπ

γmicroγπω




sum=



ii

kind

DE

ksp

DE

e

dOIMJJMc

dW

dOMJJMc

dW

rD

De

De

ωρ

ρ

γγπ

γγπω

2

2

2

2

3

3

42

h

h

Selection rules


minus harr minus )

Selection rules



Amn= 1 τ





J I

Fmin = |J ndash I|

Fmax = J + IF+1F

J I

Fmin = |J ndash I|

Fmax = J + IF+1F

Vhpf = AI JI


Lande interval rule






sum partpartpart

+minus=+=βα βα

αβmicroϕ

micro

2

6)0(

xxQeHWWW Q

F = J + I


H0 ψn(0) = E(0) ψn









sum=n

nn qcq )()( )0(ψψ




kmEE

kVmmVkE

m mkk ne

minus= sum )2(





H0 ψn(0) = E(0) ψn

(0) (H0 + V) ψ = E ψwhere E(0)

n = E(0)n


sum Ψ=Ψn

nn qcq )()( )0()0()0(


(0)(q)





n

( )sumprime

prime =minusn







0

21

22221

11211

=

minus

minusminus

EVVV

VEVVVVEV

NNNN

N

N

L

LLLL

L

L






J JJ

ZZZMJ EE

MJDMJMJDMJMJDMJE

γ γγγ

γγγγγγ 2EE



22


∆

plusmn=∆ γγ2E



M = ndash1

Jrsquo = 1

Jrsquorsquo = 0

M = 0

M = 1

M = 0

e perp Ze perp Z

e Z

ΔM=0

ΔM=plusmn1

σ - component

π - component

σ - component

Z E e





B me

2h


WB = - μ B


M = J J-1 hellip -J


++++minus+

+=JJ

SSLLJJg





Jrsquo = 0

M = 0

M = 1M = 0

e perp Ze perp Z

e ZΔM=0

ΔM=plusmn1

σndash - component

π - component

σ+ - component

Z Н e





dOnMJeJMmc

edW

dOnMJeJMmc

edW

ki

kab

ki

kem

ρρ

ρρ

γγπ

ω

γγπ

ω

2

23

2

2

23

2

2

)1(2

primeprimeprime=

+primeprimeprime=

minus kr

kr

pe

pe

h

h



( )sum +minus=



iii

kind

DM

ksp

DM

mce

dOIMJJMc

dW

dOMJJMc

dW

slM

M

M

22

42

2

2

2

2

3

3

h

r

h

r

h

ωρ

ρ

γmicroγπ

γmicroγπω




sum=



ii

kind

DE

ksp

DE

e

dOIMJJMc

dW

dOMJJMc

dW

rD

De

De

ωρ

ρ

γγπ

γγπω

2

2

2

2

3

3

42

h

h

Selection rules


minus harr minus )

Selection rules



Amn= 1 τ




H0 ψn(0) = E(0) ψn









sum=n

nn qcq )()( )0(ψψ




kmEE

kVmmVkE

m mkk ne

minus= sum )2(





H0 ψn(0) = E(0) ψn

(0) (H0 + V) ψ = E ψwhere E(0)

n = E(0)n


sum Ψ=Ψn

nn qcq )()( )0()0()0(


(0)(q)





n

( )sumprime

prime =minusn







0

21

22221

11211

=

minus

minusminus

EVVV

VEVVVVEV

NNNN

N

N

L

LLLL

L

L






J JJ

ZZZMJ EE

MJDMJMJDMJMJDMJE

γ γγγ

γγγγγγ 2EE



22


∆

plusmn=∆ γγ2E



M = ndash1

Jrsquo = 1

Jrsquorsquo = 0

M = 0

M = 1

M = 0

e perp Ze perp Z

e Z

ΔM=0

ΔM=plusmn1

σ - component

π - component

σ - component

Z E e





B me

2h


WB = - μ B


M = J J-1 hellip -J


++++minus+

+=JJ

SSLLJJg





Jrsquo = 0

M = 0

M = 1M = 0

e perp Ze perp Z

e ZΔM=0

ΔM=plusmn1

σndash - component

π - component

σ+ - component

Z Н e





dOnMJeJMmc

edW

dOnMJeJMmc

edW

ki

kab

ki

kem

ρρ

ρρ

γγπ

ω

γγπ

ω

2

23

2

2

23

2

2

)1(2

primeprimeprime=

+primeprimeprime=

minus kr

kr

pe

pe

h

h



( )sum +minus=



iii

kind

DM

ksp

DM

mce

dOIMJJMc

dW

dOMJJMc

dW

slM

M

M

22

42

2

2

2

2

3

3

h

r

h

r

h

ωρ

ρ

γmicroγπ

γmicroγπω




sum=



ii

kind

DE

ksp

DE

e

dOIMJJMc

dW

dOMJJMc

dW

rD

De

De

ωρ

ρ

γγπ

γγπω

2

2

2

2

3

3

42

h

h

Selection rules


minus harr minus )

Selection rules



Amn= 1 τ





kmEE

kVmmVkE

m mkk ne

minus= sum )2(





H0 ψn(0) = E(0) ψn

(0) (H0 + V) ψ = E ψwhere E(0)

n = E(0)n


sum Ψ=Ψn

nn qcq )()( )0()0()0(


(0)(q)





n

( )sumprime

prime =minusn







0

21

22221

11211

=

minus

minusminus

EVVV

VEVVVVEV

NNNN

N

N

L

LLLL

L

L






J JJ

ZZZMJ EE

MJDMJMJDMJMJDMJE

γ γγγ

γγγγγγ 2EE



22


∆

plusmn=∆ γγ2E



M = ndash1

Jrsquo = 1

Jrsquorsquo = 0

M = 0

M = 1

M = 0

e perp Ze perp Z

e Z

ΔM=0

ΔM=plusmn1

σ - component

π - component

σ - component

Z E e





B me

2h


WB = - μ B


M = J J-1 hellip -J


++++minus+

+=JJ

SSLLJJg





Jrsquo = 0

M = 0

M = 1M = 0

e perp Ze perp Z

e ZΔM=0

ΔM=plusmn1

σndash - component

π - component

σ+ - component

Z Н e





dOnMJeJMmc

edW

dOnMJeJMmc

edW

ki

kab

ki

kem

ρρ

ρρ

γγπ

ω

γγπ

ω

2

23

2

2

23

2

2

)1(2

primeprimeprime=

+primeprimeprime=

minus kr

kr

pe

pe

h

h



( )sum +minus=



iii

kind

DM

ksp

DM

mce

dOIMJJMc

dW

dOMJJMc

dW

slM

M

M

22

42

2

2

2

2

3

3

h

r

h

r

h

ωρ

ρ

γmicroγπ

γmicroγπω




sum=



ii

kind

DE

ksp

DE

e

dOIMJJMc

dW

dOMJJMc

dW

rD

De

De

ωρ

ρ

γγπ

γγπω

2

2

2

2

3

3

42

h

h

Selection rules


minus harr minus )

Selection rules



Amn= 1 τ





H0 ψn(0) = E(0) ψn

(0) (H0 + V) ψ = E ψwhere E(0)

n = E(0)n


sum Ψ=Ψn

nn qcq )()( )0()0()0(


(0)(q)





n

( )sumprime

prime =minusn







0

21

22221

11211

=

minus

minusminus

EVVV

VEVVVVEV

NNNN

N

N

L

LLLL

L

L






J JJ

ZZZMJ EE

MJDMJMJDMJMJDMJE

γ γγγ

γγγγγγ 2EE



22


∆

plusmn=∆ γγ2E



M = ndash1

Jrsquo = 1

Jrsquorsquo = 0

M = 0

M = 1

M = 0

e perp Ze perp Z

e Z

ΔM=0

ΔM=plusmn1

σ - component

π - component

σ - component

Z E e





B me

2h


WB = - μ B


M = J J-1 hellip -J


++++minus+

+=JJ

SSLLJJg





Jrsquo = 0

M = 0

M = 1M = 0

e perp Ze perp Z

e ZΔM=0

ΔM=plusmn1

σndash - component

π - component

σ+ - component

Z Н e





dOnMJeJMmc

edW

dOnMJeJMmc

edW

ki

kab

ki

kem

ρρ

ρρ

γγπ

ω

γγπ

ω

2

23

2

2

23

2

2

)1(2

primeprimeprime=

+primeprimeprime=

minus kr

kr

pe

pe

h

h



( )sum +minus=



iii

kind

DM

ksp

DM

mce

dOIMJJMc

dW

dOMJJMc

dW

slM

M

M

22

42

2

2

2

2

3

3

h

r

h

r

h

ωρ

ρ

γmicroγπ

γmicroγπω




sum=



ii

kind

DE

ksp

DE

e

dOIMJJMc

dW

dOMJJMc

dW

rD

De

De

ωρ

ρ

γγπ

γγπω

2

2

2

2

3

3

42

h

h

Selection rules


minus harr minus )

Selection rules



Amn= 1 τ



( )sumprime

prime =minusn







0

21

22221

11211

=

minus

minusminus

EVVV

VEVVVVEV

NNNN

N

N

L

LLLL

L

L






J JJ

ZZZMJ EE

MJDMJMJDMJMJDMJE

γ γγγ

γγγγγγ 2EE



22


∆

plusmn=∆ γγ2E



M = ndash1

Jrsquo = 1

Jrsquorsquo = 0

M = 0

M = 1

M = 0

e perp Ze perp Z

e Z

ΔM=0

ΔM=plusmn1

σ - component

π - component

σ - component

Z E e





B me

2h


WB = - μ B


M = J J-1 hellip -J


++++minus+

+=JJ

SSLLJJg





Jrsquo = 0

M = 0

M = 1M = 0

e perp Ze perp Z

e ZΔM=0

ΔM=plusmn1

σndash - component

π - component

σ+ - component

Z Н e





dOnMJeJMmc

edW

dOnMJeJMmc

edW

ki

kab

ki

kem

ρρ

ρρ

γγπ

ω

γγπ

ω

2

23

2

2

23

2

2

)1(2

primeprimeprime=

+primeprimeprime=

minus kr

kr

pe

pe

h

h



( )sum +minus=



iii

kind

DM

ksp

DM

mce

dOIMJJMc

dW

dOMJJMc

dW

slM

M

M

22

42

2

2

2

2

3

3

h

r

h

r

h

ωρ

ρ

γmicroγπ

γmicroγπω




sum=



ii

kind

DE

ksp

DE

e

dOIMJJMc

dW

dOMJJMc

dW

rD

De

De

ωρ

ρ

γγπ

γγπω

2

2

2

2

3

3

42

h

h

Selection rules


minus harr minus )

Selection rules



Amn= 1 τ







J JJ

ZZZMJ EE

MJDMJMJDMJMJDMJE

γ γγγ

γγγγγγ 2EE



22


∆

plusmn=∆ γγ2E



M = ndash1

Jrsquo = 1

Jrsquorsquo = 0

M = 0

M = 1

M = 0

e perp Ze perp Z

e Z

ΔM=0

ΔM=plusmn1

σ - component

π - component

σ - component

Z E e





B me

2h


WB = - μ B


M = J J-1 hellip -J


++++minus+

+=JJ

SSLLJJg





Jrsquo = 0

M = 0

M = 1M = 0

e perp Ze perp Z

e ZΔM=0

ΔM=plusmn1

σndash - component

π - component

σ+ - component

Z Н e





dOnMJeJMmc

edW

dOnMJeJMmc

edW

ki

kab

ki

kem

ρρ

ρρ

γγπ

ω

γγπ

ω

2

23

2

2

23

2

2

)1(2

primeprimeprime=

+primeprimeprime=

minus kr

kr

pe

pe

h

h



( )sum +minus=



iii

kind

DM

ksp

DM

mce

dOIMJJMc

dW

dOMJJMc

dW

slM

M

M

22

42

2

2

2

2

3

3

h

r

h

r

h

ωρ

ρ

γmicroγπ

γmicroγπω




sum=



ii

kind

DE

ksp

DE

e

dOIMJJMc

dW

dOMJJMc

dW

rD

De

De

ωρ

ρ

γγπ

γγπω

2

2

2

2

3

3

42

h

h

Selection rules


minus harr minus )

Selection rules



Amn= 1 τ




M = ndash1

Jrsquo = 1

Jrsquorsquo = 0

M = 0

M = 1

M = 0

e perp Ze perp Z

e Z

ΔM=0

ΔM=plusmn1

σ - component

π - component

σ - component

Z E e





B me

2h


WB = - μ B


M = J J-1 hellip -J


++++minus+

+=JJ

SSLLJJg





Jrsquo = 0

M = 0

M = 1M = 0

e perp Ze perp Z

e ZΔM=0

ΔM=plusmn1

σndash - component

π - component

σ+ - component

Z Н e





dOnMJeJMmc

edW

dOnMJeJMmc

edW

ki

kab

ki

kem

ρρ

ρρ

γγπ

ω

γγπ

ω

2

23

2

2

23

2

2

)1(2

primeprimeprime=

+primeprimeprime=

minus kr

kr

pe

pe

h

h



( )sum +minus=



iii

kind

DM

ksp

DM

mce

dOIMJJMc

dW

dOMJJMc

dW

slM

M

M

22

42

2

2

2

2

3

3

h

r

h

r

h

ωρ

ρ

γmicroγπ

γmicroγπω




sum=



ii

kind

DE

ksp

DE

e

dOIMJJMc

dW

dOMJJMc

dW

rD

De

De

ωρ

ρ

γγπ

γγπω

2

2

2

2

3

3

42

h

h

Selection rules


minus harr minus )

Selection rules



Amn= 1 τ






B me

2h


WB = - μ B


M = J J-1 hellip -J


++++minus+

+=JJ

SSLLJJg





Jrsquo = 0

M = 0

M = 1M = 0

e perp Ze perp Z

e ZΔM=0

ΔM=plusmn1

σndash - component

π - component

σ+ - component

Z Н e





dOnMJeJMmc

edW

dOnMJeJMmc

edW

ki

kab

ki

kem

ρρ

ρρ

γγπ

ω

γγπ

ω

2

23

2

2

23

2

2

)1(2

primeprimeprime=

+primeprimeprime=

minus kr

kr

pe

pe

h

h



( )sum +minus=



iii

kind

DM

ksp

DM

mce

dOIMJJMc

dW

dOMJJMc

dW

slM

M

M

22

42

2

2

2

2

3

3

h

r

h

r

h

ωρ

ρ

γmicroγπ

γmicroγπω




sum=



ii

kind

DE

ksp

DE

e

dOIMJJMc

dW

dOMJJMc

dW

rD

De

De

ωρ

ρ

γγπ

γγπω

2

2

2

2

3

3

42

h

h

Selection rules


minus harr minus )

Selection rules



Amn= 1 τ





Jrsquo = 0

M = 0

M = 1M = 0

e perp Ze perp Z

e ZΔM=0

ΔM=plusmn1

σndash - component

π - component

σ+ - component

Z Н e





dOnMJeJMmc

edW

dOnMJeJMmc

edW

ki

kab

ki

kem

ρρ

ρρ

γγπ

ω

γγπ

ω

2

23

2

2

23

2

2

)1(2

primeprimeprime=

+primeprimeprime=

minus kr

kr

pe

pe

h

h



( )sum +minus=



iii

kind

DM

ksp

DM

mce

dOIMJJMc

dW

dOMJJMc

dW

slM

M

M

22

42

2

2

2

2

3

3

h

r

h

r

h

ωρ

ρ

γmicroγπ

γmicroγπω




sum=



ii

kind

DE

ksp

DE

e

dOIMJJMc

dW

dOMJJMc

dW

rD

De

De

ωρ

ρ

γγπ

γγπω

2

2

2

2

3

3

42

h

h

Selection rules


minus harr minus )

Selection rules



Amn= 1 τ






dOnMJeJMmc

edW

dOnMJeJMmc

edW

ki

kab

ki

kem

ρρ

ρρ

γγπ

ω

γγπ

ω

2

23

2

2

23

2

2

)1(2

primeprimeprime=

+primeprimeprime=

minus kr

kr

pe

pe

h

h



( )sum +minus=



iii

kind

DM

ksp

DM

mce

dOIMJJMc

dW

dOMJJMc

dW

slM

M

M

22

42

2

2

2

2

3

3

h

r

h

r

h

ωρ

ρ

γmicroγπ

γmicroγπω




sum=



ii

kind

DE

ksp

DE

e

dOIMJJMc

dW

dOMJJMc

dW

rD

De

De

ωρ

ρ

γγπ

γγπω

2

2

2

2

3

3

42

h

h

Selection rules


minus harr minus )

Selection rules



Amn= 1 τ



( )sum +minus=



iii

kind

DM

ksp

DM

mce

dOIMJJMc

dW

dOMJJMc

dW

slM

M

M

22

42

2

2

2

2

3

3

h

r

h

r

h

ωρ

ρ

γmicroγπ

γmicroγπω




sum=



ii

kind

DE

ksp

DE

e

dOIMJJMc

dW

dOMJJMc

dW

rD

De

De

ωρ

ρ

γγπ

γγπω

2

2

2

2

3

3

42

h

h

Selection rules


minus harr minus )

Selection rules



Amn= 1 τ




Amn= 1 τ



pc iv: molecular spectroscopy / molekülspektroskopie prof

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