Winter 2018

The topics are:

1. Tensor product of state spaces; matrix representations of kets and operators

2. Entanglement

3. Operators: functions of operators, unitary operators

4. Density operator: pure states and statistical mixtures of states; thermodynamic equilibrium

5. von Neumann entropy and entanglement entropy

6. Time evolution operator

7. Schrodinger, Heisenberg and interaction pictures of QM

8. Berry's phase

9. Gauge transformations; Aharanov-Bohm effect

10. Rotations; brief description of SU(2) and non-Abelian gauge theories

11. Space and time translation operators; space inversion

12. Time reversal and unti-unitary operators; application to angular momentum;
Kramers degeneracy

13. Identical particles: exchange degeneracy, permutation operators;
symmetrisation postulate for bosons and fermions

14. Occupation numbers, occupation number kets

15. Fock space; creation and annihilation operators

16. Propagators (Green's functions); retarded propagators

17. Path integrals

Class schedule: Tuesdays and Thursdays 10:30-11:45

Textbooks: Quantum Mechanics, vols. 1 & 2 by C. Cohen-Tannoudji, B. Diu and F. Laloe, Quantum Mechanics by A. Messiah, Quantum Theory of Many Particle Systems by Fetter and Walecka

**This file created November 27, 2006; last updated on January 4, 2018.**