PHYSICS 428: QUANTUM MECHANICS III
Fall 2006
Instructor:
Prof. Michael S. Vogeley
Department of Physics
Office: Disque 811
Email: vogeley@drexel.edu
Phone: (215)895-2710
Office hours: TBA
Animation of an excited state of Hydrogen, by Drexel student Glenn Winship.
Announcements
Course Meetings
Syllabus
Course Description and Philosophy
Course Outline
Textbook and Reading Assignments
Lecture Notes
Grading
Problem Sets
Problem Set Solutions
Problem Hints
Exams
Miscellaneous
ANNOUNCEMENTS:
Solutions to problem set 5
and lecture notes 1 through 11 are posted below.
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 Fridays 10:00-11:50 a.m. in
Curtis 259. We will typically begin with an hour or so of lecture,
then work some problems in class.
Syllabus
This web page is the syllabus. Please print this out and save it
and/or bookmark this website for the future (no printed copies will be
distributed). 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. Toward the end of the second quarter you worked out the QM
description of the Hydrogen atom, from which you could first see how
the QM formulation yields accurate predictions of the observed
phenomena, and began study of multi-particle systems.
Now you're ready to delve more deeply into QM. But first we'll begin
QM III with a review of some of the basics you learned QM I and II, to
tune up our brains after the Summer (and the coop cycle). We will
then carry on with examining systems of identical particles,
including the quantum mechanical descriptions of atoms and
molecules. We'll venture outside of the textbook to discuss how
quantum mechanics governs the properties of more complicated
molecules. We will study scattering theory which describes
how particles interact with each other, as in collisions in a particle
accelerator. The Dirac equation is your introduction to
relativistic QM. We'll examine the interaction of radiation with
matter to see how absorption and emission of photons arises
from perturbation theory. Lastly, if we have time, we study the
path integral formula of quantum mechanics, a la Feynmann.
Course Outline
The first week of the course will be primarily review, so you are
well-advised to go over your notes and problems from QM I and II.
- Review of Principles and Simple Problems
- Postulates of QM, methods, fundamental equations
- From classical to QM physics
- 1-D problems and potentials
- Harmonic oscillator
- Angular momentum and rotation operators
- Central force problems and Hydrogen atom
- Spin
- Addition of Angular Momentum (Ch. 12 and Appendix B)
- Identical Particles and Atoms (Ch. 12)
- Molecules (9.7, 12.4, handouts)
- Scattering Theory (6.10, Ch. 13)
- Photons and Atoms (Radiation!) (Ch. 14)
- Relativistic Perturbations (11.6,11.7)
- The Dirac Equation (handouts)
- Path Integrals (Ch. 8)
Textbook and Reading Assignments
Required Reading: A Modern Approach to Quantum Mechanics,
by John S. Townsend, 2000, (University Science Books: Sausalito)
ISBN 1-891389-13-0.
This is the same text that was used for Quantum Mechanics I and II, so
most of you should already own it.
See the course outline above for the chapters that correspond to the new material covered in this course.
I will also hand out photocopies of selected passages from other QM
texts, as necessary to supplement Townsend.
Lecture Notes
PDF files of typeset lectures notes may be downloaded here (no paper copies will be distributed). These notes are not a substitute for reading the textbook.
Lecture notes 1 (PDF)
Also read the
Fourier notes (PDF)
Lecture notes 2 (PDF)
Lecture notes 3 (PDF)
Lecture notes 4 (PDF)
Lecture notes 5 (PDF)
Lecture notes 6 (PDF)
Lecture notes 7 (PDF)
Lecture notes 8 (PDF)
Lecture notes 9 (PDF)
Lecture notes 10 (PDF)
Lecture notes 11 (PDF)
Grading
Grades will be based on the following weighting of different
components of the course:
Problem Sets: 25%
Midterm Exam: 30%
Final Exam: 45%
Problem Sets (check for hints down below!)
There will be five problem sets (each 5% of your grade). 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.
Problem Set 1 (PDF)
Problem Set 2 (PDF)
Problem Set 3 (PDF)
Problem Set 4 (PDF)
Problem Set 5 (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
Problem Set 1:
In Problem 2, the point is that the wavefunction is
periodic, repeating over an interval of length L. This is what was
meant by the particle being "defined on an interval of length L." This
does not mean that the particle is "undefined" for x>L.
In Problem 4, I really do mean for you to find the eigenvalues (not the
eigenvectors) and to determine their magnitude. The eigenvalues may be
complex, so we want the norm of each.
Problem Set 4:
Please SOLVE for the angle in problem 2 by computing the expectation value of the position operator for both wavefunctions.
Exams
The midterm will be in class on Friday, November 3.
The final exam will be held during the usual exam week.
Both exams will be half closed and half open book.
Midterm exam solutions(PDF)
Miscellaneous
Hear Schroedinger's cat meow
Last update: December 4, 2006.