This core course covers advanced topics in non-relativistic quantum mechanics. Topics may include: Kets, Bras, and Operators; basis sets, Change of Basis and Matrix Representations; Measurements, Observables, and the Uncertainty Relations; Continuous systems: Position, Momentum, and Translation; Density Operators and Pure Versus Mixed Ensembles; entropy; Time Evolution: Schrodinger Equation; Heisenberg Picture; master equation; Schrodinger's Wave Equation; free particles; bound states; examples (square well, HO); Angular Momentum in Quantum Mechanics; Spherical symmetry and the Hydrogen Atom; Symmetries, Conservation Laws, and Degeneracies; Time-Independent Perturbation Theory; fine structure of Hydrogen; scattering; Time-Dependent Perturbation Theory: The Interaction Picture; Fermi's golden rule; Multi-Particle states; Permutation Symmetry and Pauli Principle.