Independent Study: Advanced Quantum Mechanics

 

Offered upon student request.

 

Teacher: Athanasios Petridis

                Harvey Ingham 31C

                Phone: (515) 271-3723

                E-Mail: Athan.Petridis@drake.edu

 

Class Schedule: by appointment

Textbook: Readings from several books

Homework: 1 assignment per 2 weeks.

 

The following topics are covered in the course (the list is neither inclusive or exclusive and may change from year to year or during the semester according to instructor’s view or to match student interests):

 

  1. Dirac's formalism, commutators, eigenvalue equations, expectation values.
  2. Time-independent problems using the confluent hypergeometric equation.
  3. Time-independent perturbation theory, non-degenerate and degenerate.
  4. Time dependent perturbation theory, Fermi's golden rule, and the Breit-Wigner curve.
  5. Adiabatic and sudden approximations.
  6. The WKB method and relation with the Hamilton-Jacobi theory.
  7. Green's functions, differenctial and integral equations for the kernel and the wavefunction.
  8. Eigenstate representation of Green's functions. Free-particle Green's function.
  9. Feynman diagrams.
  10. The scattering matrix, symmetries, and unitarity.
  11. Elastic and inelastic cross sections.
  12. Partial wave analysis, scattering, and resonances.