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Physics 522: Quantum Mechanics II


Course Outline


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: Tue/Thu 1:00-2:15pm

Grading weights:

Homework: 30%

Midterm exam: 30%

Final exam: 40%

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

Other useful textbooks:

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

E. Merzbacher, Quantum Mechanics, Wiley, 1997.

A. Messiah, Quantum Mechanics, Dover, 1999.

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