Physics 511---Quantum Mechanics
Course Syllabus---Fall 2008

Instructor: Prof. Steven Gottlieb
Office: Swain West 226
Phone Number:       855-0243
E-mail: sg at
Office Hours: any mutually convenient time when I am in or by appointment. This policy is designed to make it easier for you to see me. Please take advantage of it.
Grader: Hamed Shojaei
Physics 511 meet TH 10:10 a.m.--12:05 p.m. in Swain West 217.

Physics--- undergraduate Electricity and Magnetism, Classical Mechanics and Quantum Mechanics or consent of instructor
Mathematics---Elementary ordinary differential equations; matrix algebra; complex variables; Fourier analysis

Modern Quantum Mechanics by J.J. Sakurai. We are using the Revised Edition, published by Addison Wesley (1994). I expect to cover the first 3-4 chapters in P511.

You will learn the motivation for and theory of quantum mechanics. The Schr\"odinger wave function formalism and operator methods are both developed. Applications to one dimensional potential problems, the harmonic oscillator, the hydrogen atom and angular momentum are discussed.

Course Goals
1. Describe (some of) the experimental results which lead to the need for a modification to classical mechanics.
2. Explain the physical interpretation of a wave packet and the uncertainty relation.
3. Solve one- and three-dimensional potential problems by calculating eigenfunctions and eigenvalues.
4. Become confortable with the formalism of Hilbert space and linear operator theory.
5. Understand the relationship between the Schroedinger and Heisenberg formulations of quantum mechanics.
6. Perform separation of variables for the Schroedinger equation in three dimensions.
7. Understand angular momentum and rotational symmetry.

There will be assignments almost every week.

There will be two midterm exams and a final exam. The first midterm will be given approximately the 9th week of the semester and the second will be given the Tuesday before Thanksgiving.

Each midterm exam will count 20 percent of your grade. The final will count 30 percent, as will the homework.

Late Assignments
It is unwise to expect to be able to do your assignments the night before they are due. Start work early on each assignment. Homework handed in within 24 hours of time due will have 10% of the value of the assignment subtracted. Homework handed in between 24 and 48 hours late will have 20% of its value subtracted. Homework handed in later will be accepted at the discretion of the instructor and will be reduced in value by 40%.

Academic Honesty
One of the best ways to learn and to enjoy physics is by discussing it with colleagues. It is expected that you may wish to discuss the problems with others in the class. However, when you write up the homework solutions, they should come from your own head, or your own notes from a discussion, not from the written work of someone else. Naturally on the exams you will be expected to work on your own.



States of a quantum mechanical system
Kets, bras, and operators
Position and Momentum
Wave Functions

Quantum Dynamics

Time evolution and the Schrodinger equation
Schrodinger and Heisenberg Pictures
Simple Harmonic Oscillator
Path Integrals

Angular Momentum

Rotation group, Euler angles, SO(3), SU(2)
Spin-1/2 systems
Commutation Relations
Eigenstates of angular momentum
Addition of angular momentum
Clebsch-Gordon coefficients
Wigner-Eckart theorem

Symmetries (as time allows)

Conservation laws
Time reversal


*G. Baym, Lectures on Quantum Mechanics (Benjamin)

H.A. Bethe and E.E. Salpeter, Quantum Mechanics of One- and Two-Electron Atoms (Springer)

*P.A.M. Dirac, The Principles of Quantum Mechanics (Oxford)

*S. Gasiorowicz, Quantum Physics (Wiley)

*L.D. Landau and E.M. Lifshitz, Quantum Mechanics (Pergamon)

H.J. Lipkin, Quantum Mechanics (North Holland)

*E. Merzbacher, Quantum Mechanics (Wiley)

A. Messiah, Quantum Mechanics (2 volumes) (Wiley)

Roger Newton, Quantum Physics: A Text for Graduate Students (Springer Verlag)

*L.I. Schiff, Quantum Mechanics (McGraw-Hill)

*On reserve in Swain Hall Library.