Physics 661 Quantum Mechanics II Spring 2005
Lecture Notes
1. Introduction
2. Outline
3. Postulates
4. Physics
660 Review
5. V. Symmetry in Quantum Mechanics
5.1. Transformations between physically equivalent quantum
descriptions and Wigner’s Theorem
5.2. Space-Time Symmetries
5.2.1. The Principle of Galilean Relativity and the
Galilean Group
6.
5.3. Spatial Rotations, the Rotation Group and the Angular Momentum Operators
5.3.1. Geometry of rotations
and the rotation group
5.3.2. The Angular Momentum
operators and their commutation relations
5.3.3. Physical Description of
Spin
5.3.4. Angular Momentum
Commutation Relations and the “Standard Basis”
5.3.5. Angular Momentum
Operator Matrix Representation in the Standard Basis
5.3.6. Spin and Orbital Angular
Momentum Revisited
5.3.7. Addition of angular
momentum and Clebsch-Gordon coefficients
5.3.8. The Wigner-Eckhardt
theorem and Irreducible Tensor Operators
7. Addition of
Angular Momentum and Clebsch-Gordon Coefficients
8. Irreducible
Tensor Operators and the Wigner-Eckart Theorem
9. Parity and
Time Reversal Transformations
10. Rayleigh-Schroedinger Perturbation Theory
11. Brillouin-Wigner
Perturbation Theory
12. Rayleigh-Ritz
Variational Method
13. Fine Structure of the Hydrogen
Atom Spectrum
14. Hydrogen Atom in Electric and Magnetic Fields
15. Zeeman Effect
16. Stark Effect
17. Elastic Scattering Theory
18. Potential Scattering
19. Scattering Green Function
20. Born Approximation
21. Examples of Potential Scattering
22. Central Potential Scattering and Partial Wave
Analysis
23. Scattering by Complex Potentials
24. Bound States and Lippmann-Schwinger Equation
25. Born Approximation and Partial Wave Analysis
26. Examples of Partial Wave Analysis
27. Time Dependent Perturbation
Theory-Dirac Perturbation Theory
28. Fermi's Golden Rule
29. Semi-Classical Treatment of Electromagnetic Radiation
30. Formal Theory of Scattering
31. Identical Particles
32. Hartree-Fock Approximation
33. Exchange Effects In Elastic Scattering