Fall 2012

Instructor: Prof. Michael S. Vogeley
Department of Physics
Office: Disque 811
Phone: (215)895-2710
Office hours: Thursdays 2-3 and by appointment

Teaching Assistant: Vishal Kasliwal
Department of Physics
Office: Disque 808
Phone: (215)895-1544
Office hours: Wednesdays 4-5 and by appointment

We are living in a quantum world. Get used to it.

Course Meetings
Course Description and Philosophy
Course Outline
Textbook and Reading Assignments
Course rules of conduct
Problem Sets
Problem Hints
Course Schedule


Welcome back to Drexel and welcome to the home page of QM III. This is your resource page for information about the course, including homework assignments, exams, and solutions. This web page is also the syllabus for the course. To save paper, I will not print and distribute copies of documents in class. You may read them on the web or your computer and print out if you need.

Course Meetings

Lectures will be given on Mondays and Wednesdays 2:00-3:50 p.m. in Curtis 250A. Our class meetings will include lectures on the course material and problem solving. You should do the reading assignments ahead of time so that you are prepared to ask and answer questions.


This web page is the syllabus. Please print this out and save it and/or bookmark this website for the future. If you're reading a printed copy, and don't remember the URL, you can find the web page at You should check the web page frequently for updates.

Course Description and Philosophy

Quantum Mechanics (QM hereafter) is one of the foremost intellectual achievements of the 20th century and forms much of the foundation of modern Physics. Many of the giants of Physics (Einstein, Bohr, Pauli, Dirac, Feynmann, et al.) were responsible for its development. Study hard and you will be rewarded by sharing in their insight.

In the first two quarters of our three part sequence on QM, you studied the basic equations, discussed the similarities and differences between the classical and QM descriptions, and solved some simple, typically one-dimensional problems. In the second quarter you worked on QM in three dimensions, including description of the Hydrogen atom, from which you could first see how the QM formulation yields accurate predictions of the observed phenomena, and studied multi-particle systems.

Now you're ready to delve more deeply into QM. Read through the practice problems to tune up your brains after the Summer (and the coop cycle). Then we'll quickly step up to more interesting work. Most problems more complicated than those you solved in QM I and II require use of one approximation scheme or another. Clearly, learning to do Physics is more than just memorizing equations; you need to learn methods for applying them: perturbation theory and the variational principle , for example. We'll examine the interaction of radiation with matter to see how absorption and emission of photons arises from perturbation theory. Then we will study scattering theory which describes how particles interact with each other, as in collisions in a particle accelerator. We will also consider some deep questions and experiments that strike at the core of our understanding of quantum mechanics, including the EPR paradox and Bell's Theorem.

Course Outline

Not necessarily in chronological order:
  1. Review of Principles and Simple Problems
  2. Time-Independent Perturbation Theory (Ch. 6)
    • Nondegenerate Perturbation Theory
    • Degenerate Perturbation Theory
    • The Fine Structure of Hydrogen
    • The Zeeman Effect
    • Hyperfine Splitting
  3. Time-Dependent Perturbation Theory (Ch. 9)
    • Two-level systems
    • Emission and absorption of radiation (Photons!)
    • Spontaneous emission
  4. Variational Principle (Ch. 7)
    • Theory
    • Ground state of Helium
    • Hydrogen molecule ion
  5. Scattering Theory (Ch. 11)
    • Partial wave analysis
    • Phase shifts
    • Born approximation
  6. Deep Questions in Quantum Mechanics (Ch. 12)
    • EPR paradox
    • Bell's theorem
    • No-clone theorem
    • Schroedinger's cat
    • Quantum zeno paradox

Textbook and Reading Assignments

Required Reading: Introduction to Quantum Mechanics, 2nd edition by David J. Griffiths, 2005, (Pearson Prentice Hall: Upper Saddle River, NJ) ISBN 0-13-111892-7 This is the same text that was used for Quantum Mechanics I and II, so most of you should already own it. Other books that I recommend include A Modern Approach to Quantum Mechanics by John S. Townsend, Principles of Quantum Mechanics by R. Shankar, and Quantum Physics by Stephen Gasiorowicz.

See the Course Schedule for the assigned readings, which you should do before class, so that you are prepared to ask and answer questions.

I will also hand out photocopies of selected passages from other QM texts, as necessary to supplement Griffiths. Here's one from David Mermin:

Mermin on reality and quantum theory


Grades will be based on the following weighting of different components of the course:
Problem Sets: 30%
Class Participation (in-class problems): 5%
Midterm Exam 1: 20%
Midterm Exam 2: 20%
Final Exam: 25%

Course Rules of Conduct

Most of this is common sense, but some folks need a gentle reminder.

Electronic distractions: Silence your cell phone or leave it home. Only phone calls (to me) from the Nobel Prize committee will be tolerated. Laptop computers may be used only for taking notes. Web surfing, texting, reading/sending email is prohibited during class. I will ask you to leave the class if you violate this rule.

Food: Our class meetings are at lunchtime and everyone has to eat sooner or later. So, if you must bring your lunch, you may do so, provided that you can still takes notes while eating it and the smell is not unbearable (or so tasty that I'm tempted to steal it - triathletes are always hungry).

Plagiarism: Use your own very large brain (you're a physicist!) and don't even think about cheating. See homework rules below.

Problem Sets (check for hints down below!)

There will be six problem sets. You will have a week to a week and a half to complete each. No late homework will be accepted. Please neatly and accurately write up your solutions to these problems; the notation of QM is quite compact in places and small differences in the equations can have large differences in meaning. I will hand out solutions to the problems on or shortly after their due dates, to give you feedback as quickly as possible.

You may discuss the homework with your classmates, but you and you alone are responsible for the work that you turn in. Please write up your own solutions to the problems. Breaches of this policy will result in homework scores being divided by the number of ``participants.'' Second offenses may result in failure (of the class).

Use of solutions to these problems from previous years constitutes plagiarism. You must attribute (by giving the correct reference) any significant help that you receive from outside sources.

Practice Problems 1 (PDF) Just for practice - I give you the solutions!

Practice Problems 2 (PDF) Ditto.

Problem Set 1 (PDF) Due by 4:00 p.m. Friday, October 5 in the "homework hand in folder."

Problem Set 2 (PDF) Due in class Wednesday, October 17.

Problem Set 3 (PDF) Due by 4:00 p.m. Friday, October 26 in the "homework hand in folder."

Problem Set 4 (PDF) Due by 4:00 p.m. Friday, November 16 in the "homework hand in folder."

Problem Set 5 (PDF) Due by 4:00 p.m. Friday, November 30 in "homework hand in folder."

Problem Set 6 (PDF) Due by 4:00 p.m. Friday, December 7 in "homework hand in folder."
Quantum Computing with Ions (PDF)
Measuring and Manipulating Individual Quantum Systems (PDF)

Problem Set Solutions

Problem Set 1 solutions(PDF)

Problem Set 2 solutions(PDF)

Problem Set 3 solutions(PDF)

Problem Set 4 solutions(PDF)

Problem Set 5 solutions(PDF)

Problem Set 6 solutions(PDF)

Hints on Problems


Any topic covered in lecture, the assigned readings, or homeworks is fair game. I will distribute a non-exhaustive list of "questions to ponder" in advance of each exam to help guide your studying.

There will be two "midterm" exams, after weeks 4 and 8. These exams will cover material during the previous four weeks or so. Midterm 1 will be in class on 10/20 and will be half closed and half open book. Midterm 2 will be take-home, entirely open book, and will be distributed from this web site on 11/18 and due in class on 11/22.

The final exam will be held during the usual exam week, on Friday, December 14 at 8:00-10:00 a.m.. It will be comprehensive and half closed and half open book. You may bring a calculator to perform numerical calculations only.

Midterm exam solutions (PDF)

Course Schedule

Please note the following schedule of readings and assignments. This schedule may be revised, so you should recheck this web page. Notation of "HW#" indicates that a homework is due by that Friday. Exact due dates for the homework will be announced in class. You should do the indicated reading before class.

Week Class Dates Reading Homework Exams
1 September 24, 26 practice problems, Griffiths ch. 6
2 October 1, 3 Griffiths ch. 6 HW1
3 October 10 (no class 10/8) Griffiths ch. 9 HW2
4 October 15, 17 Griffiths ch. 9
5 October 22, 24 Griffiths ch. 11 HW3
6 October 29, 31 Griffiths ch. 11
7 November 5, 7 Griffiths ch. 11 Midterm exam 1 in class 11/5
8 November 12, 14 Griffiths ch. 11, 7 HW4
9 November 19 (Thanksgiving break 11/21) Griffiths ch. 7, 12
10 November 26, 28 Griffiths ch. 12 and handouts HW5
11 December 3, 5 Griffiths ch. 12 and handouts HW6
12 No Class Final Exam, TBA


Hear Schroedinger's cat meow (this one is still alive!)

Last update: December 10, 2012.