Physics 139B Home Page---Fall 2009

This page contains copies of the class handouts, and other pertinent items of interest for the U.C. Santa Cruz Physics 139B class.

Final exam solutions are posted to Section III of this website. The graded exams are available for pick-up in my office any time this week. I will be in my office most of the week in the afternoons (excluding Wednesday).

Have a great winter holiday break---you earned it!!!

The distributions of the final course grades and the final exam scores are shown in the histograms below:

[ I. General Information and Syllabus | II. Problem Sets and Exams | III. Solutions to Problem Sets and Exams | IV. Other Class Handouts | V. Articles of Interest ]

The General Information and Syllabus handout is available in either PDF or Postscript format     [PDF | Postscript]
Some of the information in this handout is reproduced here.

General Information
Instructor	Howard Haber
Office	ISB 326
Phone	459-4228
Office Hours	Mondays and Tuesdays 2--3 pm
e-mail	haber@scipp.ucsc.edu

Class Hours

Lectures: Tuesdays and Thursdays, 12:00--1:45 pm, ISB 231

Required Textbook

Introductory Quantum Mechanics, 4th Edition by Richard L. Liboff

Course Grading and Requirements

40% Homework (5 problem sets)
25% Midterm Exam (Thursday October 29, 2009, 12--1:45 pm)
35% Final Exam (Wednesday, December 9, 2009, 12--3 pm)

Homework assignments will be due on every second Thursday of the academic quarter starting with the first assignment that is due on Thursday October 8, 2009. The homework problem sets are not optional. You are encouraged to discuss the class material and homework problems with your classmates and to work in groups, but all submitted problems should represent your own work and understanding.

The final exam will be held in ISB 231. This exam will be three hours long and cover the complete course material. You must take the final exam to pass the course. You will be permitted to consult the class textbook, your own handwritten notes, and any class handout during the final exam.

Course Syllabus

1. Elements of matrix mechanics [Liboff, sections 11.1--11.5]
2. Introduction to spin [Liboff, sections 11.6--11.9]
3. Addition of angular momentum [Liboff, sections 9.4, 9.5, 11.10]
4. Quantum mechanics in an external electromagnetic field [Liboff, section 10.4 and handout]
5. Time-independent perturbation theory [Liboff, sections 13.1--13.3]
6. Applications to atomic and molecular physics [Liboff, sections 12.1--12.7]
7. Time-dependent perturbation theory [Liboff, sections 8.8, 13.5--13.8]
8. Quantum theory of scattering [Liboff, sections 14.1--14.6]
9. Quantum theory of radiation [Liboff, sections 10.7, 13.9]

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Problem sets and exams are available in either PDF or Postscript formats.

• Problem Set #1--due: Thursday, October 8, 2009     [PDF | Postscript]
• Problem Set #2--due: Thursday, October 22, 2009     [PDF | Postscript]
• Midterm Exam: Thursday, October 29, 2009     [PDF | Postscript]
• Problem Set #3--due: Thursday, November 5, 2009     [PDF | Postscript]
• Problem Set #4--due: Thursday, November 19, 2009     [PDF | Postscript]
• Problem Set #5--due: Thursday, December 3, 2009     [PDF | Postscript]
• Final Exam: Wednesday, December 9, 2009     [PDF | Postscript]

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The problem set and exam solutions are available in either PDF or postscript formats.

• Solutions to Problem Set #1     [PDF | Postscript]
• Solutions to Problem Set #2     [PDF | Postscript]
• Solutions to the Midterm Exam     [PDF | Postscript]
• Solutions to Problem Set #3     [PDF | Postscript]
• Solutions to Problem Set #4     [PDF | Postscript]
• Solutions to Problem Set #5     [PDF | Postscript]
• Solutions to the Final Exam     [PDF | Postscript]

• I present the calculation of the ground state energy of the helium atom using the variational principle. A trial wave function is presented that depends on a parameter Z, and then the expectation value of the Hamiltonian with respect to the trial wave function is evaluated as a function of Z. Details of all the steps in the calculation are provided (along with a number of integration tricks) here:     [PDF | Postscript]
  
  
• In the computation of the fine structure of hydrogen, we need to evaluate the expectation values <1/r^n> (n=1,2,3) with respect to the hydrogen atom radial wave functions. A clever way of doing this is provided by Supplement 8A to Gasiorowicz's textbook (see the following item), which can be found here:     [PDF].
  
  
• The book by Stephen Gasiorowicz, Quantum Physics, 3rd Edition (John Wiley & Sons, Inc., Hoboken, NJ, 2003) includes free supplemental material on the Wiley website. Here, I provide Gasiorowicz's Supplement 16A on the Aharonov-Bohm effect     [PDF].
  
  
• As Liboff presents only a minimal discussion of the Schrodinger equation for a charged particle in an external electromagnetic field, I have written up some more detailed notes on this topic, which can be found here:     [PDF | Postscript]
  
  
• A nice set of notes by Frank Porter of Caltech discusses the fundamental role of the electromagnetic vector potential and the Aharonov-Bohm effect. These note can be found here: [PDF | Postscript]
  Solutions to the problems given at the end of Porter's notes can be found here: [PDF | Postscript]
  
  
• A table of Clebsch-Gordon coefficients is provided courtesy of the Review of of Particle Physics, published by the Particle Data Group in Physics Letters B667 (2008) 1--1340.    [PDF]
  
  
• A nice review of vectors and matrices has been provided courtesy of Michael Dine and can be found here:     [PDF | Postscript]
  
  

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• In 1977, J.D. Jackson gave a colloquium in which he explained the connection between the fundamental intrinsic magnetic dipole moment and the hyperfine structure of the s-states of the hydrogen atom. His derivation differs somewhat from the one I gave in class, but of course the results are the same. Jackson provided a writeup of his colloquium as a CERN Yellow Report (CERN 77-17), which you can find here:   [PDF]
  
  
• The following paper shows how to add two spin-1/2 angular momenta by representing each spin as a vector lying in three-dimensional space, but with a vector addition law that takes into account the quantum mechanical fluctuations.   [PDF | Postscript]
  
  
• A more sophisticated treatment of the graphical representation for the quantum mechanical addition of two angular momenta can be found here:   [PDF]
  
  

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