Quantum Mechanics Ii

AY2018/2019 Semester 1

This course introduces the framework and basic tenets of quantum mechanics. Review of introductory quantum mechanics: wavefunction and uncertainty principle, Schrodinger equation, one-dimensional examples (square well, harmonic oscillator, periodic potential) Formalism of quantum mechanics: state of a system, dynamical variables and operators, expansions in eigenfunctions, commutation, unitary transformations, matrix representations, time evolution, Schrodinger and Heisenberg pictures, path integrals, symmetry principles and conservation laws, the classical limit. Angular momentum: orbital angular momentum and spatial rotations, eigenvalues and eigenfunctions, particle on a sphere and rigid rotator, general angular momentum, matrix representations, spin and total angular momentum, addition of angular momentum. Schrodinger equation in 3 dimensions: separation of variables, central potentials, free particle, 3-D square well, hydrogenic atoms, 3-D isotropic oscillator. Approximation methods: Time-independent perturbation theory for non-degenerate and degenerate levels, variational method, WKB approximation, time-dependent perturbation theory.