Review of Quantum Mechanics





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Course Contents

Problem oriented review of Quantum Mechanics. Historical development of quantum mechanics, wave packets, Schrödinger's equation, two level systems. Solution (analytical and numerical) of time independent Schrödinger equation for various physically relevant potentials; angular momentum algebra, spherical harmonics. Numerical solution of the radial Schrödinger equation for arbitrary spherically symmetric potential. Equivalence of Heisenberg approach and Schrödinger approach; matrix mechanics. Quantization of electromagnetic field in a cavity and in free space. Approximation methods: perturbation theory and variation principle for time independent problems, WKB approximation. Time dependent Schrödinger equation. Time dependent perturbation theory and matter radiation interaction. Selection rules for dipole radiation. Adiabatic and sudden approximations. Topics in

(i) scattering theory,

(ii) relativistic quantum mechanics,

(ii) introduction to path integral formulation,

(iv) identical particles.

Problems of current interest, many body physics.





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