1. Graduate Quantum Mechanics I (PHY 651)-Fall 2022-2026
Course content:
A thorough study of the linear vector space, Hilbert space, Dirac notation, and eigenvalue problems, including diagonalization.
Review of classical mechanics (Poisson bracket, Lagrange, and Hamiltonian EOM).
The postulates of QM, time-dependent and time-independent Schrödinger equation.
Various potential problems including particle in a box, step potential, attractive delta potential, and simple harmonic oscillator.
Second quantization
Angular momentum algebra: A general formalism of angular momentum, orbital and spin angular momentum.
3D problems in spherical coordinates -- electron in a central potential.
The addition of angular momenta and the Clebsch-Gordan coefficient.
Introduction of quantum entanglement.
Textbooks:
R. Shankar, Principles of Quantum Mechanics, 2nd Edition from Springer
Quantum Mechanics -Concept and Application by N. Zettili from Wiley