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