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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) xp > h/2 x - uncertainty of position p - uncertainty of momentum Et > h/2 E - uncertainty of energy t - uncertainty of time TOC Heisenberg Uncertainty Principle xp > h/2 Et > 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? Et > 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) xp > 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