PH-603  Advanced Quantum Mechanics

1. Quantum mechanics of continuous systems, discretization, infinite matrices, calculation of matrix elements between states characterized by continuous variables.
2. Concept of classical paths, principle of least action, introduction to path integrals, propagator, simple harmonic oscillator in path integral representation. 
3. Adiabatic processes, Berry phase in atomic and molecular physics, quantum Hall effect, coherent states.
4. Multiple vacua, tunneling phenomena, imaginary time in quantum mechanics, instantons, spontaneous symmetry breaking.
5. Bosons and fermions and their relation to spin. Permutational symmetry. Slater determinant for many-fermion systems, Thouless’s theorem, anyons and fractional statistics.  Supersymmetric quantum mechanics.
6. Superconductivity and superfluidity: Meisner effect, Landau-Ginsburg theory, Cooper pairs.
7. Basics of many body theory, particles and holes, RPA, Feynman diagrams for non-relativistic systems.
8. Quantum theory of measurement, EPR paradox, Bell’s theorem, quantum logic, quantum computation.

Recommended texts:

• Principles of Quantum Mechanics, R.Shankar, 2nd edition, (Springer, 1994).
• A Guide To Feynman Diagrams In The Many-body Problem, Richard D. Mattuck, (Dover, 1992).
• Advanced Quantum Mechanics, J.J. Sakurai, (Addison-Wesley).