Quantum physics

1. Quantum physics 1900 Planck Quantum theory 1913 Bohr Quantum mechanics 1924 Werner Heisenberg, with Max Born and Pascual Jordan, discovered matrix mechanics, the first version of quantum mechanics. Erwin Schrödinger invented wave mechanics, a second form of quantum mechanics Dirac laid the foundations of quantum field theory

2. A physics quantity missing in quantum mechanics? Temperature

3. References 1. Max Tegmark and John Archibald Wheeler 100 Years of QUANTUM MYSTERIES Scientific American v284 no2 68-75 (2001) 2. Daniel Kleppner and Roman Jackiw. One Hundred Years of Quantum Physics Science v 289, no5481 (2000)893-898 3. SLAC THE FUTURE OF THE QUANTUM THEORY

4. David J. Griffiths: Introduction to Quantum Mechanics, 2nd ed. Eugen Merzbacher:Quantum Mechanics, 3rd ed. WKB Approximation Schiff: Quantum Mechanics well of finite depth Practical quantum mechanics gravitational well Bohm, A Messiah, D ter Haar P A. Dirac:Principles of Quantum Mechanics, 4th ed 钱伯初、张永德、曾谨言、苏如铿、 ……

5. Stern-Gerlach experiment and spin

7. The magnetic moment reads In classical picture, orbital moment is

8. Magnetic moment in a nonuniform magnetic field will encounter a force (besides torque) Classical mechanics, … , predicted that the atomic magnets would precess in the field but remain randomly oriented, so the deflections would only broaden (but not split) the beam. According to quantum theory mL~ Lz ~ mh splits into 2l+1 inB

9. In 1922, O. Stern and W. Gerlach to measure the magnetic moment of silver atoms. But they found the beam splits into two components. 2l+1=2? N.B. The idea of electron spin angular momentum. was introduced by Uhlenbeck and Goudsmit in 1925.

10. ), but that the state m = 0 was somehow suppressed so that only two instead of the expected Then Ag atom was known in a p-state ( traces were observed. This assumption, unnatural and ad hoc though it was, accounted for the duplicity of traces and for the measured value of the magnetic moment. Bohr, among others, had become uneasy that his model excluded a zero value.

11. A curious historical puzzle remains. The earliest attribution of the splitting to spin that we have found did not appear until 1927, when Ronald Fraser noted that the ground-state orbital angular momentum and associated magnetic moments of silver, hydrogen, and sodium are zero. So in 1922 the intrepid experimenters had no idea it was spin that they had discovered.

12. OTTO STERN for his contribution to the development of the molecular ray method and his discovery of the magnetic moment of the proton.

13. In 1925 Uhlenbeck and Goudsmit introduced the idea of electron spin angular momentum. For electron, the spin Smay have values: and Spin is an intrinsic angular momentum. It is never associated with angular coordinates. It is a nature of elementary particles. Unlike mass and charge, there is no classical analog to spin!

14. the concept of electron spin … Bohr was deeply skeptical. In December, he traveled to Leiden, the Netherlands, to attend the jubilee of Hendrik A. Lorentz's doctorate. Pauli met the train at Hamburg, Germany, to find out Bohr's opinion about the possibility of electron spin. Bohr said the proposal was "very, very interesting," his well-known put-down phrase. Later at Leiden, Einstein and Paul Ehrenfest met Bohr's train, also to discuss spin. There, Bohr explained his objection, but Einstein showed a way around it and converted Bohr into a supporter.

15. On his return journey, Bohr met with yet more discussants. When the train passed through Gottingen, Germany, Heisenberg and Jordan were waiting at the station to ask his opinion. And at the Berlin station, Pauli was waiting, having traveled especially from Hamburg. Bohr told them all that the discovery of electron spin was a great advance.

16. How the spin interprets the fine structure?

17. In electron system

19. Forn = 2, it is 4.53×10–5eV The observed split of Lymanais 4.54×10–5eV Too good to believe.

20. • • But the following effects have not be taken into account Substantially spin is relativistic effect. In Dirac equation it appears naturally.

21. Electron never spins. a uniform ball of charge e and of radius of classical electron radius r0 when spins with angular velocity w

22. Let it equal to electron’s spin magnetic moment: (i.e. assume the spin magnetic moment is caused by such mechanism) It means that the surface speed is hundred times of light speed. Whereas for classical theory, substantial disaster is radiation due to acceleration rather than high speed.

23. Electromagnetic theory, though, predicted that orbiting electrons would continuously radiate away their energy and spiral into the nucleus in about a trillionth of a second. Of course, hydrogen atoms were known to be eminently stable. Indeed, this discrepancy was the worst quantitative failure in the history of physics—under-predicting the lifetime of hydrogen by some 40 orders of magnitude.

24. Potential barrier In classical case, only particle of energy higher than U0 can go over the barrier.

25. But for waves,

27. For microscopic particles, barrier ForNH3 Potential energy for SHM well

29. Stationary Schrödinger equations are Define We have

30. The solution is right traveling

31. usually we are only interested in reflection and transmission coefficients In barrier penetrating problem, Even for E < U0 ( k22 < 0 ), we still can find finite T. This is so-called tunneling Set 隧道穿透

32. Using “matching condition” at x = 0, a, that is, yandy'continuous, we have

33. Example 24.1 Eugen Merzbacher. Quantum Mechanics, 3rd edWKB approximation

34. Exact definition: For example

35. tunnel diode