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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)
TOC
Schrödinger and the quantum atom
Schrödinger solves  for hydrogen atom
The electron is represented by a probability wave
2 = probability
TOC
Schrödinger and the quantum atom
Only calculate probability of finding electron
Electron “clouds”
TOC
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
TOC
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
TOC
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
TOC
The Einstein-Bohr debate
Einstein would challenge Bohr at conferences
Front: Bohr, Heisenberg, Pauli, Stern, Meitner, Ladenburg
For example…
TOC
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
TOC
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
TOC