Contents:•Copenhagen Interpretation of Young’s Double slit•The Quantum atom •Heisenberg uncertainty principle•The Einstein Bohr debate•Quantum Mechanics

                                                               

Quantum mechanics and the Copenhagen Interpretation

Copenhagen Interpretation

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•Demo of Young’s double slit (monochromatic light)•Electrons have a “wavelength” = h/p•Electrons interfere too

Copenhagen Interpretation

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•Electrons interfere even when sent one at a time (why?)•Copenhagen: = Schrödinger wave function of electron•“Probability waves” interfere (2 = probability)

Schrödinger and the quantum atom

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Schrödinger solves for hydrogen atomThe electron is represented by a probability wave2 = probability

Schrödinger and the quantum atom

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Only calculate probability of finding electronElectron “clouds”

Heisenberg Uncertainty Principle

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Let’s find an electronPhoton changes the momentum of

electronx

p h/ (smaller , bigger p)

xp > h/2

x - uncertainty of position p - uncertainty of momentum

Et > h/2

E - uncertainty of energy t - uncertainty of time

Heisenberg Uncertainty Principle

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xp > h/2

Et > h/2

Strange quantum effects:• Observation affects reality• Energy is not conserved (for t)• Non determinism • Quantum randomness• Quantum electrodynamics

Whiteboards: Heisenberg Uncertainty

1 | 2

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t = 2.1 x 10-16 s W

Et > h/2

(5.0 x 10-19 J)t > h/2

t = 2.1 x 10-16 s

For what period of time is the uncertainty of the energy of an electron 5.0 x 10-19 J?

v = 8.3 x 105 m/s W

xp > h/2

p = mvm = 9.11 x 10-31 kg(.14 x 10-9 m)p > (6.626 x 10-34 Js)/2p = 7.5 x 10-25 kg m/sp = mv(7.5 x 10-25 kg m/s) = (9.11 x 10-31 kg)vv = 8.3 x 105 m/s

If the uncertainty of an electron’s position is .14 nm, what is the minimum uncertainty of its velocity? (3)

The Einstein-Bohr debate

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Einstein objected to quantum randomness“God does not play dice”

Attacked either Heisenberg uncertainty, or complementarity

The Einstein-Bohr debate

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Einstein would challenge Bohr at conferences

Front: Bohr, Heisenberg, Pauli, Stern, Meitner, Ladenburg

For example…

Gedanken experiment (to disprove complementarity)

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•Detect which slit the electron went through with light beam (particle behaviour)•If interference pattern appears, then we have both wave and particle behaviour•Complementarity says it must be either

s

d

Electron beam

Bohr would take a walk

E. Fermi, N. Bohr

Bohr’s reply

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•No interference pattern would happen

s

d

Electron beam

•The light that detected the electron would change its momentum•To have interference, electrons must be monochromatic = h/p•Complementarity is intact

Quantum mechanics

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Three “types” of physics• Newtonian/classical - big stuff• Relativity - speeds close to c• Quantum mechanics - physics of the atom

• Correspondence principle

Bohr always prevailed

(God apparently does play dice)