Advanced Quantum Mechanics (PY 781/782)
The text is Principles of Quantum Mechanics by R. Shankar.
Chapters in grey are not covered. Green entries are additional material.
PY 781
DETAILED SYLLABUS
- 1. Mathematical Introduction (vector spaces, operators, the eigenvalue
problem)
- 2. Review of Classical Mechanics
- 3. All is Not Well with Classical Mechanics
- 4. The Postulates
- 5. Simple Problems in One Dimension
- 6. The Classical Limit
- 7. The Harmonic Oscillator
- 9. The Heisenberg Uncertainty Relations
- 10. Systems with N Degrees of Freedom
- 11. Symmetries and their Consequences
- 12. Rotational Invariance and Angular Momentum
- Wigner Rotation matrices
- 13. The Hydrogen Atom
PY 782
DETAILED SYLLABUS
- 14. Spin
- The EPR Paradox and Bell's Theorem
- 15. Addition of Angular Momentum
- Spin Systems
- 16. Variational and WKB Methods
- 17. Time Independent Perturbation Theory
- 18. Time-dependent Perturbation Theory
- 19. Scattering Theory
- Variational Scattering Methods
- Lippmann-Schwinger Formalism and Green's Functions
- Final State Interactions
- Bound State Scattering
- 8. The Path Integral Formulation of Quantum Theory
- Path Integrals in Curved Space and Operator Ordering
- 21. Path Integrals II
- 20. The Dirac Equation
- Second Quantization
In addition to learning quantum mechanics, we will be learning some of the
tools that every physicist needs to know before graduation. Specifically:
- Maple
- A maple primer postscript file
- A guide to Maple guides
- this one's pretty good.
- LaTex
- Fortran
- gnuplot
- Unix
Some other things the well educated physicist may have occasion to learn:
Some special functions of use to
people doing Quantum Mechanics.