PHYSICS 428: QUANTUM MECHANICS III

PHYSICS 428: QUANTUM MECHANICS III
Fall 2008

Instructor: Prof. Michael S. Vogeley
Department of Physics
Office: Disque 811
Email: vogeley@drexel.edu
Phone: (215)895-2710
Office hours: Wednesday 2:00-4:00 p.m. (and by appointment)

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Announcements
Course Meetings
Syllabus
Course Description and Philosophy
Course Outline
Textbook and Reading Assignments
Grading
Problem Sets
Problem Set Solutions
Problem Hints
Exams
Course Schedule
Miscellaneous

ANNOUNCEMENTS:

Midterm 2 solutions are posted below.

Problem Set 6 is posted below. It is due in class on Friday, December 5. I will post the solutions on Friday. This problem set will count as "extra credit" in the sense that I will use it to drop your lowest homework score (percentage-wise).

The final exam is on Monday, December 8 at 10:30-12:30 in CAT 75 (wherever that is). "Questions to ponder" will be distributed shortly.

Course Meetings

Lectures will be given on Wednesdays and Fridays 9:00-10:50 a.m. Just to keep you on your toes (and in shape from climbing the stairs), we'll meet in two different rooms: Curtis 352 on Wednesdays, Curtis 457 on Fridays. 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.

Syllabus

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 http://www.physics.drexel.edu/courses/Physics-428. 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 (Deep Questions will include attendance at Grad Quantum III with Prof. Gilmore):
  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.

Grading

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%

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)

Practice Problems 2 (PDF)

Problem Set 1 (PDF)

Problem Set 2 (PDF)

Problem Set 3 (PDF)

Problem Set 4 (PDF)

Problem Set 5 (PDF)

Problem Set 6 (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)

Hints on Problems


Exams


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 in-class "midterm" exams, at the ends of the 4th and 8th weeks. These exams will cover material during the previous four weeks or so.

The final exam will be held during the usual exam week. It will be comprehensive.

All exams will be half closed and half open book.

Midterm exam solutions (PDF)

Midterm exam 2 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 that Friday at the start of class. 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 8, 10 Griffiths ch. 6 HW2
4 October 15, 17 Griffiths ch. 9 HW3
5 October 22 (no class on 10/24) Griffiths ch. 12 Midterm Exam 1 on 10/22
6 October 27, 29, 31 (attend Grad QMIII) ch. 12 HW4
7 November 5, 7 Griffiths ch. 11
8 November 12, 14 Griffiths ch. 11 HW5
9 November 19, 21 Griffiths ch. 7 Midterm 2 handed out on 11/21
10 No class - Thanksgiving break
11 December 3, 5 Griffiths ch. 12 and Handouts HW6
12 No Class Final Exam, TBA

Miscellaneous


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

Last update: December 1, 2008.