Course Description: This is a 3-credit course offered to first-year PhD students, serving as a comprehensive review of key topics in quantum mechanics. The course covers the following topics: 1. Bound state solutions of the hydrogen atom 2. Theory of angular momentum: - Clebsch-Gordan coefficients - Wigner-Eckart theorem 3. Time-independent perturbation theory: - Applications to the harmonic oscillator - Stark effect - Zeeman effect 4. Time-dependent perturbation theory: - Rabi oscillations - Fermi's golden rule - Ionization, absorption, and emission processes 5. Scattering theory: - T-matrix formalism - Lippmann-Schwinger equation - Born approximation - Partial wave analysis - Scattering states of the hydrogen atom 6. Relativistic quantum mechanics: - Klein-Gordon equation - Scalar field theory.