Quantum mechanics and the
Copenhagen Interpretation
Contents:
•Copenhagen Interpretation of
Young’s Double slit
•The Quantum atom
•Heisenberg uncertainty principle
•The Einstein Bohr debate
•Quantum Mechanics
Copenhagen Interpretation
•Demo of Young’s double slit (monochromatic light)
•Electrons have a “wavelength”  = h/p
•Electrons interfere too
TOC
Copenhagen Interpretation
•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
Schrödinger solves  for hydrogen atom
The electron is represented by a probability wave
2 = probability
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Schrödinger and the quantum atom
Only calculate probability of finding electron
Electron “clouds”
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Heisenberg Uncertainty Principle
Let’s find an electron
Photon changes the momentum of
electron
x  
p  h/ (smaller , bigger p)
xp > h/2
x - uncertainty of position
p - uncertainty of momentum
Et > h/2
E - uncertainty of energy
t - uncertainty of time
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Heisenberg Uncertainty Principle
xp > h/2
Et > h/2
Strange quantum effects:
• Observation affects reality
• Energy is not conserved (for t)
• Non determinism
• Quantum randomness
• Quantum electrodynamics
TOC
Whiteboards:
Heisenberg Uncertainty
1|2
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For what period of time is the
uncertainty of the energy of an
electron 5.0 x 10-19 J?
Et > h/2
(5.0 x 10-19 J)t > h/2
t = 2.1 x 10-16 s
t = 2.1 x 10-16 s
W
If the uncertainty of an electron’s position
is .14 nm, what is the minimum
uncertainty of its velocity? (3)
xp > h/2
p = mv
m = 9.11 x 10-31 kg
(.14 x 10-9 m)p > (6.626 x 10-34 Js)/2
p = 7.5 x 10-25 kg m/s
p = mv
(7.5 x 10-25 kg m/s) = (9.11 x 10-31 kg)v
v = 8.3 x 105 m/s
v = 8.3 x 105 m/s
W
The Einstein-Bohr debate
Einstein objected to quantum randomness
“God does not play dice”
Attacked either Heisenberg uncertainty, or
complementarity
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The Einstein-Bohr debate
Einstein would challenge Bohr at conferences
Front: Bohr, Heisenberg, Pauli, Stern, Meitner, Ladenburg
For example…
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Gedanken experiment (to disprove complementarity)
Electron beam
s
d
•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
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Bohr would take a walk
E. Fermi, N. Bohr
Bohr’s reply
Electron beam
s
d
•No interference
pattern would happen
•The light that detected
the electron would
change its momentum
•To have interference,
electrons must be
monochromatic
• = h/p
•Complementarity is
intact
TOC
Quantum mechanics
Bohr always prevailed
(God apparently does play dice)
Three “types” of physics
• Newtonian/classical - big stuff
• Relativity - speeds close to c
• Quantum mechanics - physics of the atom
• Correspondence principle
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