Contents: Copenhagen Interpretation of Young’s Double slit The Quantum atom Heisenberg uncertainty...
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Transcript of Contents: Copenhagen Interpretation of Young’s Double slit The Quantum atom Heisenberg uncertainty...
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
TOC
•Demo of Young’s double slit (monochromatic light)•Electrons have a “wavelength” = h/p•Electrons interfere too
Copenhagen Interpretation
TOC
•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
TOC
Schrödinger solves for hydrogen atomThe electron is represented by a probability wave2 = probability
Schrödinger and the quantum atom
TOC
Only calculate probability of finding electronElectron “clouds”
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
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
Whiteboards: Heisenberg Uncertainty
1 | 2
TOC
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
TOC
Einstein objected to quantum randomness“God does not play dice”
Attacked either Heisenberg uncertainty, or complementarity
The Einstein-Bohr debate
TOC
Einstein would challenge Bohr at conferences
Front: Bohr, Heisenberg, Pauli, Stern, Meitner, Ladenburg
For example…
Gedanken experiment (to disprove complementarity)
TOC
•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
TOC
•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
TOC
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)