the classical limit

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IntroductionUltraviolet catastrohpe

Photoelectric effectWave-particle duality

The Classical Limit

A brief review of three phenomena that lead to quantummechanics

C. Nikolás Cruz C.Level 6 / Academic SkillsBrewster Technical Center

November 14, 2014

Nikolás Cruz The Classical Limit

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Outline

1 IntroductionClassical physicsQuantum physics

2 Ultraviolet catastrohpe

BlackbodyRayleigh-Jeans lawWien approximationPlank’s law

3 Photoelectric effectHertz’s experimentClassical expectationsQuantum explanation

4 Wave-particle duality


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Classical physicsQuantum physics

How would you define classical physics?


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Classical physics

Classical physics has numerous branches, for example:

Classical mechanics

Classical electrodynamics

Classical thermodynamics

Classical statistical mechanics

Special relativity and general relativity

Classical chaos theory and nonlinear dynamics


I d

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Classical physics


Classical mechanics







I d i

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Classical physics


Classical mechanics







I t d ti

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Classical physics


Classical mechanics







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Introduction


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Classical physics


Classical mechanics







Introduction

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Quantum physics

What have you heard about Quantum Mechanics?

What do you know about Quantum Mechanics?

What does it mean to be quantum?


Introduction

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Quantum physics





Introduction

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Ultraviolet catastrohpePhotoelectric effect

Wave-particle duality


Quantum physics





Introduction

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Quantum = quanta


Introduction

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I will talk about this...

Just kidding.


IntroductionUl i l h Cl i l h i

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Purpose of the talk

Learn about three physical phenomena that are unable to explainbased on classical physics.


IntroductionUlt i l t t t h

BlackbodyR l i h J l

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Rayleigh-Jeans lawWien approximationPlank’s law

Blackbody

A blackbody in thermal equilibrium has two notable properties:

It is an ideal emitter: at every frequency, it emits as muchenergy as any other body at the same temperature or evenmore energy.

It is a diffuse emitter: the energy is radiated isotropically,independent of direction.



BlackbodyRayleigh Jeans law

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Figure: An approximate realization of a blackbody as a tiny hole in aninsulated enclosure.



BlackbodyRayleigh Jeans law

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Rayleigh-Jeans law

B λ (T ) = 2ckT λ4

; B ν (T ) = 2ν 2kT c 2

B λ (T ) ∝ T

λ4 ; B ν (T ) ∝ ν

2T

νλ = c



BlackbodyRayleigh-Jeans law

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Rayleigh Jeans lawWien approximationPlank’s law

Figure: Ultraviolet catastrophe




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Rayleigh Jeans lawWien approximationPlank’s law

Wien approximation

B λ (T ) = 2hc 2

λ5 e −

hc

λkT ; B ν (T ) = 2hν 3

c 2 e −

hν

kT

B λ (T ) ∝ e −

hc

λkT

λ5 ; B ν (T ) ∝ ν

3e −hν

kT

hc

k = constant ;

h

k = constant




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pPhotoelectric effect


y gWien approximationPlank’s law

Figure: comparison between Wien approximation, Rayleigh-Jeans law andPlank’s law.




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pPhotoelectric effect


y gWien approximationPlank’s law

Plank’s law

Max Planck




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Wien approximationPlank’s law

Plank’s law

B λ (T ) = 2hc 2

λ5

1

e hc

λkT − 1

; B ν (T ) = 2hν 3

c 2

1

e hν

kT − 1

B λ (T ) ∝ 1

λ51

e hc

λkT − 1; B ν (T ) ∝

ν 3

e hν

kT − 1hc

k

= constant ; h

k

= constant



Ph l i ff

BlackbodyRayleigh-Jeans lawWi i i

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Plank’s law

Figure: Plank’s law spectrum.



Ph t l t i ff t

BlackbodyRayleigh-Jeans lawWi i ti

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Plank’s law approximations

If kT hν → 1

e hν

kT − 1≈

1hν

kT

= kT

hν (Rayleigh − Jeans )

If kT hν → 1

e hν

kT − 1≈ e −

hν

kT (Wien)



Photoelectric effect

Hertz’s experimentClassical expectations

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pQuantum explanation






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Quantum explanation

Hertz’s experiment





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Quantum explanation

Classical expectations

Changes in amplitude or wavelength of light would inducechanges in the rate of emission of electrons.

Even a dim light can produce the effect, but it has a lag timebetween the incidence and the emission.




Hertz’s experimentClassical expectationsQ l i

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Quantum explanation

Quantum explanation

Albert Einstein




Hertz’s experimentClassical expectationsQ t l ti

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Wave-particle dualityQuantum explanation

K max = hν − φ




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Aristotle Democritus




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Isaac Newton Christiaan Huygens Thomas Young




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James Clerk Maxwell

∇ · E = ρ

ε0

∇ · B = 0

∇× E = −∂ B

∂ t

∇× B = µ0 J + ε0µ0∂ E

∂ t



Photoelectric effectW i l d li

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Max Planck Albert Einstein



Photoelectric effectW ti l d lit

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Photoelectric effectWave particle duality

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http://en.wikipedia.org/wiki/File:

Wave-particle_duality.ogv

http://en.wikipedia.org/wiki/File:Wave-particle_duality.ogvhttp://en.wikipedia.org/wiki/File:Wave-particle_duality.ogvhttp://en.wikipedia.org/wiki/File:Wave-particle_duality.ogvhttp://en.wikipedia.org/wiki/File:Wave-particle_duality.ogvhttp://find/

the classical limit

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