Introduction: course overview, history of quantum mechanics
Mathematical foundation of quantum mechanics: quantum states and Hilbert spaces, observables and operators, commutation relations and Heisenberg's uncertainty principle, pure and mixed states, density operator
Quantum dynamics: time evolution and the Schrödinger equation, Schroedinger and Heisenberg pictures, quantization of harmonic oscillator, propagators and Feynman path integrals, potential and gauge transformation
Theory of angular momentum: rotation and angular momentum operator, spin and SU(2) group, orbital angular momentum, solution of the hydrogen atom (Schrödinger equation for central potential), addition of angular momenta and Clebsch-Gordan coefficients, tensor operators and Wigner-Eckart theorem
Symmetry in quantum mechanics: conservation laws and degeneracies, parity (space inversion), time-reversal symmetry
All information is representative only, and is likely to change from year to year.