1. 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

2. Copenhagen Interpretation TOC Demo of Young’s double slit (monochromatic light) Electrons have a “wavelength” = h/p Electrons interfere too

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

4. Schrödinger and the quantum atom TOC Schrödinger solves  for hydrogen atom The electron is represented by a probability wave  2 = probability

5. Schrödinger and the quantum atom TOC Only calculate probability of finding electron Electron “clouds”

6. Heisenberg Uncertainty Principle TOC Let’s find an electron Photon changes the momentum of electron  x   p  h / (smaller, bigger p) xp > h/2xp > h/2  x - uncertainty of position  p - uncertainty of momentum Et > h/2Et > h/2  E - uncertainty of energy  t - uncertainty of time

7. Heisenberg Uncertainty Principle TOC xp > h/2Et > h/2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

8. Whiteboards: Heisenberg Uncertainty 11 | 22 TOC

9.  t = 2.1 x 10 -16 s W Et > h/2Et > 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?

10. v = 8.3 x 10 5 m/s W xp > h/2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 10 5 m/s If the uncertainty of an electron’s position is.14 nm, what is the minimum uncertainty of its velocity? (3)

11. The Einstein-Bohr debate TOC Einstein objected to quantum randomness “God does not play dice” Attacked either Heisenberg uncertainty, or complementarity

12. The Einstein-Bohr debate TOC Einstein would challenge Bohr at conferences Front: Bohr, Heisenberg, Pauli, Stern, Meitner, Ladenburg For example…

13. 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

14. Bohr would take a walk E. Fermi, N. Bohr

15. 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

16. 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)