PHYSICS 326: QUANTUM MECHANICS I
Fall 2007
Instructor:
Prof. Michael S. Vogeley
Department of Physics
Office: Disque 811
Email: vogeley@drexel.edu
Phone: (215)895-2710
Office hours: Wednesday 3:00-4:30 p.m. , Thursday 2:30-3:30 p.m.
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
Extra Notes
Grading
Problem Sets
Problem Set Solutions
Problem Hints
Exams
Course Schedule
Miscellaneous
ANNOUNCEMENTS:
QMI is over. Enjoy your vacation and I'll see you in January for Quantum II!. Solutions to the final exam are posted below.
Welcome to the home page of QM I. 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 12:00-1:50 p.m. in Disque 919 (Monday) and Disque 109 (Friday). Our class meetings will be a mix of lecture and problem
solving.
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-326. 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 this first quarter of our three part sequence on QM, you will study
the basic equations, discussed the similarities and differences
between the classical and QM descriptions, and solve some simple,
typically one-dimensional problems. In the second quarter, we'll move
on to three dimensional problems, and 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 begin study
of multi-particle systems and perturbation theory. In the final
quarter, we'll delve into more advanced topics include the variational
principle, WKB approximation, scattering theory, and a deeper look at
the interpretation of QM.
Course Outline
Here are the topics we'll cover in QM I
- The Wave Function (Ch. 1)
- The Schroedinger Equation
- Statistical Interpretation
- Probability
- Normalization
- Momentum
- The Uncertainty Principle
- The Time-Independent Schroedinger Equation (Ch. 2)
- Stationary States
- Infinite Square Well
- Harmonic Oscillator
- Free Particle
- Delta-Function Potential
- Finite Square Well
- Formalism of Quantum Mechanics (Ch. 3)
- Hilbert Space
- Observables
- Eigenfunctions of a Hermitian Operator
- Generalized Statistical Interpretation
- Uncertainty Principle
- Dirac Notation
- Schroedinger Equation in Three Dimensions (Ch. 4.1)
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 text will also be used for Quantum Mechanics II and III, so
buy it!
See the course outline above for the chapters that correspond to the material covered in this course.
I will also hand out photocopies of selected passages from other QM
texts, as necessary to supplement Griffiths.
Extra Notes
This is a brief (5 page) review of important Fourier transform
properties and their relation to the free-particle wavefunction:
Fourier notes (PDF)
Grading
Grades will be based on the following weighting of different
components of the course:
Final Exam: 40%
Problem Sets: 30%
Midterm Exam: 25%
Class Participation: 5%
Problem Sets (check for hints down below!)
There will be eight 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.
Problem Set 1 (Due Friday, October 5):
Griffiths 1.5, 1.8, 1.11, 1.14, 1.18
Problem Set 2 (Due Friday, October 12):
Griffiths 2.2, 2.5, 2.7, 2.38
Problem Set 3 (Due Friday, October 19):
Griffiths 2.11, 2.12, 2.15, 2.42
Problem Set 4 (Due Friday, October 26):
Griffiths 1.17, 2.8, 2.14, 2.17
Problem Set 5 (Due Friday, November 9):
Griffiths 2.18, 2.19, 2.20, 2.22
Problem Set 6 (Due Friday, November 16):
Griffiths 2.29, 2.34, 2.35, 2.52
Problem Set 7 (Due Friday, November 30):
Griffiths 2.45, 2.46, 3.3, 3.4
Problem Set 8 (Due Friday, December 7):
Griffiths 3.27, 3.30, 3.34, 3.37
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)
Problem Set 7 solutions(PDF)
Problem Set 8 solutions(PDF)
Hints on Problems
Problem set 1, problem 1.8: It is not necessary
to look ahead to what we've started to learn from chapter 2. Instead,
take the lazy man's approach to proving the result: test to see if a
wave function with that extra time dependence is indeed a solution to
the time-dependent Schroedinger equation.
Exams
The midterm will be in class on Monday, October 29.
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)
Final 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 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, 28 |
1.1-1.6 |
|
|
| 2 |
October 1, 5 |
2.1, 2.2 |
HW1 |
|
| 3 |
October 12 |
2.3 |
HW2 |
|
| 4 |
October 15, 19 |
2.4 |
HW3 |
|
| 5 |
October 22, 26 |
2.5 |
HW4 |
|
| 6 |
October 29, November 2 |
2.6 |
|
Midterm in class 10/29 |
| 7 |
November 5, 9 |
3.1 |
HW5 |
|
| 8 |
November 12, 16 |
3.2, 3.3 |
HW6 |
|
| 9 |
November 19 |
3.4, 3.5 |
|
|
| 10 |
November 26, 30 |
3.6 |
HW7 |
|
| 11 |
December 3, 7 |
4.1 |
HW8 |
|
| 12 |
No Class |
|
|
Final Exam, TBA |
Miscellaneous
Hear Schroedinger's cat meow (He's still alive!)
Last update: December 17, 2007