1. Theory of Angular Momentum
Rotations and angular momentum, spin-1/2 systems and finite rotations, Euler rotations, eigenvalues and eigenstates of angular momentum, spin and orbital angular momenta, addition of angular momenta.
2. Symmetry in Quantum Mechanics
Symmetries, conservation laws, and degeneracies. Detailed analysis of discrete symmetries: parity (or space inversion), lattice translation, and the time-reversal.
3. Approximation Methods
Nondegenerate time-independent perturbation theory and its application in the harmonic oscillator, quadratic stark effect. Degenerate time-independent perturbation theory and its applications to linear Stark effect, spin-orbit interaction and fine structure, Zeeman effect. Time-dependent potentials and interaction picture, time-dependent perturbation theory and its applications to interactions with the classical radiation field. Description and applications of variational methods and the WKB approximation.
4. Scattering Theory
The Lippmann-Schwinger equation, the Born approximation, optical theorem. Free-particle states: plane wave versus spherical waves. Method of partial waves, low-energy scattering and bound states, resonance scattering.
5. Identical Particles
Permutation symmetry, symmetrization postulate, two-electron system, the Helium atom, permutation symmetry, and Young tableaux.
References
J. J. Sakurai, Modern Quantum Mechanics, Second Edition, Pearson.
R. Shankar, Principles of Quantum Mechanics, Second Edition, Springer.
E. Merzbacher, Quantum Mechanics, Third Edition, Wiley.
K. Gottfried, Quantum Mechanics, Second Edition, Springer.
A. Messiah, Quantum Mechanics (Vol. I & II), Dover Publications Inc.
Claude Cohen-Tannoudji, Bernard Diu, Frank Laloe, Quantum Mechanics (Vol. I & II), Wiley.
Richard P. Feynman, The Feynman Lectures on Physics (Vol. III), Pearson.
L. D. Landau and E.M. Lifshitz, Quantum Mechanics, Third Edition, Butterworth-Heinemann.
Leonard I. Schiff, Quantum Mechanics, Fourth Edition, McGraw Hill Education.
S. Weinberg, Lectures on Quantum Mechanics, Second Edition, Cambridge University Press.
Assignments
Examinations