Review of Basic Concepts: Review of experiments, De Broglie’s hypothesis, wave particles duality, statistical in interpretation of matter waves, probability density.

Mathematical Foundation of Quantum Mechanics: Observable and operators, state of a system (postulate-3), Hilbert space and Dirac notation, expectation values, Hermitian operators and their properties, Heisenberg uncertainty principle and superposition.

Schrödinger Equation: Time independent Schrödinger equation; general properties of one dimensional Schrödinger equation, infinite finite potential well (generalized to 3D), the harmonic oscillator (generalized to 3D), unbound states, one dimensional barrier problems, tunneling. Time dependant Schrödinger equation; time development of state function (postulate 4), expectation values and conservation laws.

Central Field Problems: Schrödinger equation in 3D for central potential, angular momentum, eigenfunctions of angular momentum, eigenvalues of orbital angular momentum, operators L2 and Lz.

Spin: Stern Gerlach experiment, symmetry principles, Pauli spin matrices, spin angular momentum, addition of angular momenta, spin orbit coupling.

Recommended Text:
1. Richard L. Liboff; “Introductory Quantum Mechanics”, 4th Edition, Pearson Education, Inc. (2003)
2. Fayyazuddin, Riazuddin; “Quantum Mechanics”, 1st Edition, World Scientific Publishing Co. Pte. Ltd. (1990).
3. J. S. Townsend; “A Modern Approach to Quantum Mechanics”, McGraw Hill Book Company, Singapore (1992).
4. W. Greiner; “Quantum Mechanics: An Introduction” Springer Verlag, Berlin (1989).
5. Sara M. McMurray; “Quantum Mechanics” Addison – Wesley Publishing Company Inc. (1994).
6. M. P. Khanna; “Quantum Mechanics”, Har-Anand Publications, New Delhi, (1996).