Phys 784

Quantum Mechanics II

Time and Location

Tuesday, 4:30 pm-7:10 pm, 01/22-05/15, Robinson Hall B105

Office hours

Tuesday and Thursday 2:00-3:00 pm or by appointment, Planetary Hall, Rm 207

Textbook

For the sake of continuity, I will continue to loosely follow the book

Modern Quantum Mechanics, 2nd Edition, J. J. Sakurai, and J. J. Napolitano

and cover chapter 5 to 7 (Berry phase and Dirac equation are covered in QM I). Materials from other sources will also be used. I find myself frequently consulting Landau and Lifshitz, Quantum Mechanics as well as Weinberg, Lectures on Quantum Mechanics.

Homework

Set 1, due Feb 12

Set 2, due Mar 5

Set 3, due Mar 26

Set 4, due Apr 18

Set 5, due Apr 30

Set 6.

Grades

Homework (50%) + Midterm (25%) + Final exam (25%)

There will be 6 sets of homeworks. They are graded on a coarse level: Excellent (5), Very Good (4), Fair (3), Absent (0). Solutions will be posted.

Both exams will be open book, take-home.

Prerequisites & Course Goals

This course continues from Phys 684, Quantum Mechanics I (chapter 1 to 4 of Sakurai). We will apply the principles you learned from 684 to solve important problems found in AMO, condensed matter, and nuclear/particle physics. Most of these problems cannot be solved exactly, so we will focus on the art of approximations. Each approximation method will be illustrated by working out examples in detail (in class and in homeworks). We will also develop the basic concepts and techniques to treat many-body quantum systems, because the world has many particles!

Topics

1. Semiclassical expansion (WKB), bound states and BS quantization rule, tunneling

2.  Time-independent perturbation theory: 1st and 2nd order, level repulsion, projection operators, lift of degeneracy, Stark effect, fine structure of H atom

3.  Time-dependent perturbation theory: interaction picture, Dyson series, constant and harmonic perturbation, transition rate and Fermi’s golden rule, photoelectric effect

4.  Scattering theory: S and T matrix, Lippmann-Schwinger Eq, Green function, cross section, Born approximation, partial waves, phase shifts, scattering length, resonance and bound states

5.  Identical particles, second quantization, interacting fermi gas, Helium atom and variational methods

6.  Quantization of electromagnetic field, photon states, Casimir effect, spontaneous emission