** **

**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

**Typical Organization**

Lectures T Th 1:00 - 2:15 PM

Homework (30%)

Midterm Exam (30%)

Final exam (40%)

Main Text: J.J. Sakurai,** ***Modern Quantum Mechanics* (Addison-Wesley, 2010)

Other Texts:

R. Shankar, *Principles of Quantum Mechanics*, Springer, 1994 (2nd Ed.)

E. Merzbacher, *Quantum Mechanic*s, Wiley, 1997.

A. Messiah, *Quantum Mechanics*, Dover, 1999.

*All information is representative only, and is likely to change from year to year.*