Quantum Mechanics

1. Review of the basics of quantum mechanics, postulates of quantum mechanics, Schrodinger/Heisenberg/interaction pictures, two-level systems and the Bloch sphere

2. Relation between quantum and classical mechanics, the Feynman path-integral representation

3. Many-body systems, second quantization, path-integral representation for many-particle systems, quantum Monte Carlo and the fermionic sign problem

4. Bogoliubov theory of weakly interacting bosons

5. Pure states versus mixed states, density operator, reduced density operator, entanglement, (maybe: EPR paradox and Bell's theorem)

6. Open quantum systems, operator-sum representation, quantum measurements, Lindblad representation, Born-Markov master equation