PHYSICS 327: QUANTUM MECHANICS II
Winter 2008

Instructor: Prof. Michael S. Vogeley
Department of Physics
Office: Disque 811
Email: vogeley@drexel.edu
Phone: (215)895-2710
Office hours: Wednesday 3:00-5:00 p.m. and by appointment

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
Grading
Problem Sets
Problem Set Solutions
Problem Hints
Exams
Course Schedule
Miscellaneous

ANNOUNCEMENTS:

Solutions to the final exam are posted below.

Welcome to the home page of QM II. 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 Tuesdays and Thursdays 12:30-2:20 p.m. in Disque 919 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-327. 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 second quarter of our three part sequence on QM, 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.

Course Outline


Here are the topics we'll cover in QM II

  1. Quantum Mechanics in Three Dimensions (Ch. 4)
  2. Identical Particles (Ch. 5)

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.

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 or any other source constitutes plagiarism. You must attribute (by giving the correct reference) any significant help that you receive from outside sources.

Problem Set 1 (Due Thursday, January 17):
Griffiths 4.3, 4.8, 4.9, 4.38 and the following:
Find the l=0 energy and total wave function (radial and angular parts together and properly normalized) of a particle of mass m that is subject to the central potential V(r)=0 in the region from r=a to r=b and V=infinity elsewhere (below r=a and above r=b), thus the particle is trapped in a cavity between two hard spheres.

Problem Set 2 (Due Thursday, January 24):
Griffiths 4.11, 4.13, 4.17, and the following:
(a) For the following cases, calculate the value of r at which the radial probability density of the hydrogen atom reaches its maximum: (i) n=1, l=0, m=0 (ii) n=2, l=1, m=0 (iii) l=n-1, m=0
(b) Compare the values obtained with the Bohr radius for circular orbits.

Problem Set 3 (Due Thursday, January 31):
Griffiths 4.18, 4.22, 4.27, 4.28, 4.57

Problem Set 4 (Due Thursday, February 7):
Griffiths 4.34, 4.49, 4.52, 4.55 and the following:
For a particle with spin s=1/2, find the eigenvectors and eigenvalues of the operator S_x + S_y.

Problem Set 5 (Due Thursday, February 21):
Griffiths 5.4, 5.5, 5.6 and two problems in the following PDF document: Problem Set 5 assignment (PDF)

Problem Set 6 (Due Thursday, February 28):
Griffiths 5.7, 5.33, and three more problems in the following PDF document: Problem Set 6 assignment (PDF)

Problem Set 7 (Due Thursday, March 6):
Griffiths 5.16, 5.17, 5.34, 5.35 (see Homework Hints below re problem 5.35).

Problem Set 8 (Due Thursday, March 13):
Griffiths 5.22, 5.23, 5.24, 5.30

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, 4.9: You've solved this before! See 2.29 from Quantum 1, problem set 6.

Problem set 7, 5.35: In (a) use Eq. 5.45 to write the total energy in terms of N, q, and m. In part (b) you can compute the total (negative!) gravitational energy of a uniform sphere by considering how much work must be done to add an amount of mass m to the star (this work is negative) and then integrating. You should get E=-(16 \pi^2 \rho^2 R^5 G/15) where \rho is the density of the star. In part (c), add up the two energy terms and find the minimum by taking the derivative (duh). Then plug in all the numbers and check that you get the given answer. In part (d), the mass of the Sun is 1.989 X 10^{30} kg. In part (e), there are 1.602 X 10^{-19} Joules/eV. The rest energy of an electron is 0.511 MeV (memorize this!).

Exams


The midterm will be in class on Tuesday, February 12.

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. REVISION TO THE TABLE BELOW: We're only going to cover up through chapter 5, so save chapter 6 for summer reading!

Week Class Dates Reading Homework Exams
1 January 8, 10 4.1
2 January 15, 17 4.2 HW1
3 January 22, 24 4.3, 4.4 HW2
4 January 29, 31 4.4 HW3
5 February 5, 7 5.1, 5.2 HW4
6 February 12, 14 5.2, 5.3 Midterm in class 2/12
7 February 19, 21 5.4 HW5
8 February 26, 28 6.1, 6.2 HW6
9 March 4, 6 6.2, 6.3 HW7
10 March 11, 13 6.3, 6.4 HW8
11 No Class Final Exam, TBA

Miscellaneous


Hear Schroedinger's cat meow (He's still alive!)

Last update: March 24, 2008