COPENHAGEN QUANTUM MECHANICS

Heisenberg: Mathematics is sense! That’s what sense is!Bohr: But in the end, in the end, remember, we have to be able to explain it all to Margrethe!

PEOPLE REVIEW

Max Plank 1858-1947 Albert Einstein 1879-1955 Neils Bohr 1885-1962 Werner Heisenberg 1901-1976 Erwin Schrödinger 1887-1961

WHAT IS QUANTUM, AND IS IT AS BAD AS THE JAMES BOND FILM?

A Quantum is defined as the smallest bit of anything

Quantum Mechanics= Mechanics of the very small

Not even science can explain how terrible Quantum of Solace was

SOME SIMPLE QUANTUM MECHANICAL SYSTEMS

Special Relativity- E2=p2c2+m2c4

Planck- E=hf For a massless particle, E=pc ʎf=c Gives us: ʎ=h/p Early 20s, deBroglie proposed that any

mass would correspond to a wavelength 1929, deBroglie Nobel Prize

1926, Erwin Schrödinger creates equation that predicts this wave deBroglie predicted Ψ(x,y,z,t)Could be used for any particleFundamental equation of ALL quantum mechanics

Güten tag.ich heiße Erwin Schrödinger

A CLOSER LOOK

iħ=( )(reduced Planck’s constant) d/dt = Time derivative Ψ(r,t) = Wave function = Laplacian function V(r,t)= Potential Energy

CLASSICAL VERSUS QUANTUM

http://tinyurl.com/c8t3e94

Classical: A Quantum: B-F Probability to find the particle in any

one spot is equal classically and particle can have any value

Probability to find the particle in any one spot is not equal at the quantum level

Confines wavelength to ʎn=2l/n

INTERPRETATIONS OF THE WAVE FUNCTION

Interpretation 1: “Ok, wow, that’s kinda gross”

Interpretation 2: Calculus? Yes. Interpretation 3: “But Chris, what does

that imply?”

TUNNELING

Objects move through barriers

Probability to find the wavefunction on the opposite side of the barrier is not zero

HYDROGEN ATOM

Probable positions of electrons are not exactly set

Based on energy levels

DISTINCTION BETWEEN LARGE AND SMALL

None of this could happen on the visible scale “it becomes important to remember that

science is concerned only with observable things and that we can observe an object only by letting it interact with some outside influence” -Dirac

This interaction, observation, causes a disturbance on the quantum scale

Traditional causality only applies to undisturbed systems

NO CATS WERE HARMED IN THE MAKING OF THIS PHYSICS

THE UNCERTAINTY PRINCIPLE?

Werner Heisenberg 1925-1926

Values of position and momentum cannot both be precisely known.

Measuring one with greater precision lowers the accuracy of the other

BOHR EINSTEIN DEBATES

God does not play dice.

Stop telling God what to do.

EINSTEIN’S BOX- 1930

Box of mass “m” with a clock that controls a shutter

Box releases a photon in some arbitrary time t creating a change in mass

E=mc2 gives precise energy

THE DOUBLE SLIT EXPERIMENT

http://tinyurl.com/yzttx3

Wave particle duality

Electrons interfere with themselves as waves but strike the detector as particles