**PH-603 Advanced Quantum Mechanics**

- Quantum mechanics of continuous systems, discretization, infinite matrices, calculation of matrix elements between states characterized by continuous variables.
- Concept of classical paths, principle of least action, introduction to path integrals, propagator, simple harmonic oscillator in path integral representation.
- Adiabatic processes, Berry phase in atomic and molecular physics, quantum Hall effect, coherent states.
- Multiple vacua, tunneling phenomena, imaginary time in quantum mechanics, instantons, spontaneous symmetry breaking.
- 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.
- Superconductivity and superfluidity: Meisner effect, Landau-Ginsburg theory, Cooper pairs.
- Basics of many body theory, particles and holes, RPA, Feynman diagrams for non-relativistic systems.
- 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).