Syllabus

1. A brief review of complex variable techniques we’ll need later in the course, in particular, Contour Integration.

2.  Spherical Tensors, the Wigner-Eckart theorem.

3. Variational Methods: trial wave functions to determine upper bounds on energies.

4. The WKB Approximation: tunneling probabilities, semiclassical quantization.

5. Time-Independent Perturbation Theory.  Examples: the Peierls Transition, van der Waals forces.

6. Time-Dependent Perturbation Theory.  Sudden and Adiabatic Approximations.

7. The Periodic Perturbation.  Two-State System.  The Golden Rule.

8. The Photoelectric Effect in Hydrogen: deriving the rate for a classical electromagnetic field.

9. Quantizing the Radiation Field.  Spontaneous Emission.

10. Scattering Theory. Born Approximation. Expansion of Plane Wave in Spherical Waves. Optical Theorem, Scattering Length, Resonances.

11. Dirac Equation. Deriving the Electron’s Magnetic Moment. Antimatter.

12. Berry Phase and Dirac Equation in Condensed Matter.