Quantum Physics I

1. Class Materials

2. Class Materials

3. Class Materials

4. Quantum mechanics as a framework. Defining linearity

5. Linearity and nonlinear theories. Schrödinger's equation

6. Necessity of complex numbers

7. Photons and the loss of determinism

8. The nature of superposition. Mach-Zehnder interferometer

9. More on superposition. General state of a photon and spin states

10. Entanglement

11. Mach-Zehnder interferometers and beam splitters

12. Interferometer and interference

13. Elitzur-Vaidman bombs

14. The photoelectric effect

15. Units of h and Compton wavelength of particles

16. Compton Scattering

17. de Broglie’s proposal

18. de Broglie wavelength in different frames

19. Galilean transformation of ordinary waves

20. The frequency of a matter wave

21. Group velocity and stationary phase approximation

22. Motion of a wave-packet

23. The wave for a free particle

24. Momentum operator, energy operator, and a differential equation

25. Free Schrödinger equation

26. The general Schrödinger equation. x, p commutator

27. Commutators, matrices, and 3-dimensional Schrödinger equation

28. Interpretation of the wavefunction

29. Normalizable wavefunctions and the question of time evolution

30. Is probability conserved? Hermiticity of the Hamiltonian

31. Probability current and current conservation

32. Three dimensional current and conservation

33. Wavepackets and Fourier representation

34. Reality condition in Fourier transforms

35. Widths and uncertainties

36. Shape changes in a wave

37. Time evolution of a free particle wavepacket

38. Fourier transforms and delta functions

39. Parseval identity

40. Three-dimensional Fourier transforms

41. Expectation values of operators

42. Time dependence of expectation values

43. Expectation value of Hermitian operators

44. Eigenfunctions of a Hermitian operator

45. Completeness of eigenvectors and measurement postulate

46. Consistency condition. Particle on a circle

47. Defining uncertainty

48. Uncertainty and eigenstates

49. Stationary states: key equations

50. Expectation values on stationary states

51. Comments on the spectrum and continuity conditions

52. Solving particle on a circle

53. Energy eigenstates for particle on a circle

54. Infinite square well energy eigenstates

55. Nodes and symmetries of the infinite square well eigenstates

56. Finite square well. Setting up the problem

57. Finite square well energy eigenstates

58. Nondegeneracy of bound states in 1D. Real solutions

59. Potentials that satisfy V(-x) = V(x)

60. Qualitative insights: Local de Broglie wavelength