Syllabus
Approximation methods: Variational methods, WKB approximation; time-indepdndent perturbation theory; time-dependent perturbation theory: Interaction picture, Fermi's golden rule, sudden and adiabatic approximations.
Scattering theory: Transition rates and cross sections, Lippmann-Schwinger equation, scattering amplitude, Green's functions; Born approximation; phase shifts and partial waves.
Symmetries in quantum mechanics: Continuous symmetries: space and time translations, rotations; rotation group and its irreducible representations; Irreducible spherical tensor operators, Wigner-Eckart theorem. Discrete symetries: parity and time reversal.
Identical particles: Meaning of identity and consequences; symmetric and antisymmetric wavefunctions; Slater determinant.
Relativistic Quantum Mechancis: Klein-Gordon equation; Dirac equation, free particle solution, electromagnetic interaction of the Dirac particle, spin and magnetic moment of the electron.
Special topics: Path integral formalism; basics of quantum information: entanglement, Einstein-Podolsky-Rosen paradox, Bell's inequality, coherent states.
Text Books
1. J. J. Sakurai, Modern Quantum Mechanics, Addison-Wesley.
2. R. Shankar, Principles of Quantum Mechanics, Springer.
3. C. Cohen-Tannoudji, et al., Quantum Mechanics, Wiley-Interscience.
4. A Peres, Quantum Theory: Concepts and Methods, Kluwer Academic Publishers.
References
Information Not Available