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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
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Copenhagen Interpretation
TOC
•Demo of Young’s double slit (monochromatic light)•Electrons have a “wavelength” = h/p•Electrons interfere too
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Copenhagen Interpretation
TOC
•Electrons interfere even when sent one at a time (why?)•Copenhagen: = Schrödinger wave function of electron•“Probability waves” interfere (2 = probability)
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Schrödinger and the quantum atom
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Schrödinger solves for hydrogen atomThe electron is represented by a probability wave2 = probability
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Schrödinger and the quantum atom
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Only calculate probability of finding electronElectron “clouds”
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Heisenberg Uncertainty Principle
TOC
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
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Heisenberg Uncertainty Principle
TOC
xp > h/2
Et > h/2
Strange quantum effects:• Observation affects reality• Energy is not conserved (for t)• Non determinism • Quantum randomness• Quantum electrodynamics
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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?
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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)
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The Einstein-Bohr debate
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Einstein objected to quantum randomness“God does not play dice”
Attacked either Heisenberg uncertainty, or complementarity
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The Einstein-Bohr debate
TOC
Einstein would challenge Bohr at conferences
Front: Bohr, Heisenberg, Pauli, Stern, Meitner, Ladenburg
For example…
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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
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Bohr would take a walk
E. Fermi, N. Bohr
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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
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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)