__ COURSE TIME:__ TuTh 10:30-11:50 am.

__ COURSE LOCATION:__ Physics-Geology 185.

__ INSTRUCTOR:__ Richard Scalettar

__ OFFICE:__ Physics-Geology 409.

__ OFFICE HOURS:__ TuTh noon-1:00 pm; or by appointment.

__ PROBLEM SESSION:__ Monday noon - 1:00 pm, Physics 416;
Attendence is * OPTIONAL *!

__ GRADING: __

5-6 Problems Sets, 60%, due Thursdays.

Midterm Exam, Thursday February 6, in class, 15%

Final Exam, Friday March 21, 6:00-8:00 pm, 25%

__ TEXT:__
We will follow Prof. Cheng's Physics 215A recommendation of
"Modern Quantum Mechanics," by J. J. Sakurai,
Revised Edition, and "Principles of Quantum Mechanics," by R. Shankar,
2nd Edition. As with 215A,
we will not follow exactly the order
of these books but much of the emphasis will be similar.

__ DISCUSSION LEADER:__ Kara Farnsworth

__ OFFICE:__ Physics/Geology 434

__ OFFICE HOURS:__ Wednesday 1:00-2:00 pm.

SYLLABUS:

This is a continuation of the first year graduate sequence in quantum mechanics. One of our goals will be to introduce some modern quantum mechanics problems in addition to the more foundational `historic' material. We will begin by reviewing and building on material from Physics 215A:

* Heisenberg Hamiltonian (illustrates addition of angular momentum, matrix picture of QM, and introduces an important model in quantum magnetism)

* Entanglement entropy (an application of density matrices and introduces a new tool to explore "quantum phase transitions")

* path integral for harmonic oscillator in "imaginary time" (builds on intro given in 215A, emphasizes connection to statistical mechanics).

and then turn to new material, covering:

* Hydrogen atom

* Time independent perturbation theory

* "Tight Binding" Hamiltonians (another illustration of matrix picture of quantum mechanics, central model of energy bands in solids)

* Time dependent perturbation theory

* Scattering theory.

LECTURE NOTES

Course Introduction and 215A Review

Heisenberg Model 1

Heisenberg Model 2

Eigenspectrum of Tridiagonal Matrices

Density Matrix Review

Entanglement Entropy

Introduction to the Bethe Ansatz (article)

Hydrogen Atom 1

Hydrogen Atom 2

Easier (?!) 3D QM problems

Sturm-Liouville Theory

Perturbation theory

Classical Scattering (see also perturbation theory pp 2-3)

Experiments on spin chains

Talk at DARPA OLE meeting on emulation of quantum spin chains

Fine Structure of Hydrogen

QM virial theorem

Generating functions

Time Dependent Perturbation Theory

Feynman Disentangling Theorem

Density of States

Atomic Lifetimes

Scattering Theory 1

Phase Shifts

Born Approximation

Scattering Summary

PROBLEM SETS AND SOLUTIONS

Problem Set 1

Problem Set 1 Solutions

Problem Set 2

Problem Set 2 Solutions

Problem Set 3

Problem Set 3 Solutions

Midterm Exam

Midterm Exam Solutions

Problem Set 4

Problem Set 4 Solutions

Problem Set 5

Problem Set 5 Solutions

Final Exam and Solutions

SOME PROBLEM SETS AND EXAMS FROM A PAST 215B COURSE I TAUGHT.

It has been quite a while since I taught 215B, these are the assignments I managed to find. We will not follow these very closely, but they are a guide to some of the material we will cover.

Problem Set 1 (1997)

Problem Set 3 (1998)

Problem Set 4 (1998)

Problem Set 5 (1997)

Problem Set 6 (1997)

Midterm Exam (1998)

Final Exam (1998)