PHYS 401 (3-0-3) Quantum Mechanics
Solutions of some one dimensional systems: step potentials, finite potential barrier, the square well, multiple square wells, the harmonic oscillator, normalization of H.Osc, wave functions, H.Osc. operator method. The formal structure of Q.M: Postulates of Q.M. commuting operators, linear vector spaces, the Schmidt orthogonalization procedure, linear transformations of linear operators, the matrix form of the eigenvalue problems, unitary transformation, application of matrix mechanics to H.Osc. The wave equation in three-dimensions: the angular momentum operators and their eigenvalues and eigenfunctions, normalization of the angular momentum, the parity operator. Spin, addition of angular momenta and identical particles : spin in Schrödinger formulation, spin orbit interaction, the vector model, identical particles. Approximation methods and applications: perturbation theory for degenerate and non-degenerate states, time dependent perturbation theory, the variational method, the JWKB approximation.
Prerequisite: PHYS 301