Quantum Physics III

1. Class Materials

2. Class Materials

3. Class Materials

4. L1.1 General problem. Non-degenerate perturbation theory

5. L1.2 Setting up the perturbative equations

6. L1.3 Calculating the energy corrections

7. L1.4 First order correction to the state. Second order correction to energy

8. L2.1 Remarks and validity of the perturbation series

9. L2.2 Anharmonic Oscillator via a quartic perturbation

10. L2.3 Degenerate Perturbation theory: Example and setup

11. L2.4 Degenerate Perturbation Theory: Leading energy corrections

12. L3.1 Remarks on a 'good basis'

13. L3.2 Degeneracy resolved to first order; state and energy corrections

14. L3.3 Degeneracy resolved to second order

15. L3.4 Degeneracy resolved to second order (continued)

16. L4.1 Scales and zeroth-order spectrum

17. L4.2 The uncoupled and coupled basis states for the spectrum

18. L4.3 The Pauli equation for the electron in an electromagnetic field

19. L4.4 Dirac equation for the electron and hydrogen Hamiltonian

20. L5.1 Evaluating the Darwin correction

21. L5.2 Interpretation of the Darwin correction from nonlocality

22. L5.3 The relativistic correction

23. L5.4 Spin-orbit correction

24. L5.5 Assembling the fine-structure corrections

25. L6.1 Zeeman effect and fine structure

26. L6.2 Weak-field Zeeman effect; general structure

27. L6.3 Weak-field Zeeman effect; the projection lemma

28. L6.4 Strong-field Zeeman

29. L6.5 Semiclassical approximation and local de Broglie wavelength

30. L7.1 The WKB approximation scheme

31. L7.2 Approximate WKB solutions

32. L7.3 Validity of the WKB approximation

33. L7.4 Connection formula stated and example

34. L8.1 Airy functions as integrals in the complex plane

35. L8.2 Asymptotic expansions of Airy functions

36. L8.3 Deriving the connection formulae

37. L8.4 Deriving the connection formulae (continued) logical arrows

38. L9.1 The interaction picture and time evolution

39. L9.2 The interaction picture equation in an orthonormal basis

40. L9.3 Example: Instantaneous transitions in a two-level system

41. L9.4 Setting up perturbation theory

42. L10.1 Box regularization: density of states for the continuum

43. L10.2 Transitions with a constant perturbation

44. L10.3 Integrating over the continuum to find Fermi's Golden Rule

45. L10.4 Autoionization transitions

46. L11.1 Harmonic transitions between discrete states

47. L11.2 Transition rates for stimulated emission and absorption processes

48. L11.3 Ionization of hydrogen: conditions of validity, initial and final states

49. L11.4 Ionization of hydrogen: matrix element for transition

50. L12.1 Ionization rate for hydrogen: final result

51. L12.2 Light and atoms with two levels, qualitative analysis

52. L12.3 Einstein's argument: the need for spontaneous emission

53. L12.4 Einstein's argument: B and A coefficients

54. L12.5 Atom-light interactions: dipole operator

55. L13.1 Transition rates induced by thermal radiation

56. L13.2 Transition rates induced by thermal radiation (continued)

57. L13.3 Einstein's B and A coefficients determined. Lifetimes and selection rules

58. L13.4 Charged particles in EM fields: potentials and gauge invariance

59. L13.5 Charged particles in EM fields: Schrodinger equation

60. L14.1 Gauge invariance of the Schrödinger Equation