Physics 466
Mathematical Methods of Theoretical Physics

Problem session 3:30 pm on Wednesday, Dec. 17th, room 184.

    Mathematical Methods for Theoretical Physics (466-001)

    Fall 2003 Tuesdays and Thursdays from 17:45 to 19:00 in room 184. My e-mail address is My office is room 176, and my phone number is 277-5318. My office hours are by appointment. But in fact whenever you see me, I am available for questions about this course.

    The grader is Mr. Ramesh Babu Laghumavarapu. His e-mail address is

    There will be a final exam. For students who do better on the homework than on the final exam, the homework will count 75%, and the final will count 25%. For students who do better on the final, the homework and the final will each count 50%.

    My notes are available as photocopies in the glassed-in front office, room 100, and as the pdf files pages 1-35, pages 36-70, pages 71-105, pages 106-139, pages 140-184, pages 185-215 (on Lie algebras), pages 216-230, pages 231-239, and examples of contour integration. I am grateful to Capt. Babani, the U.S. Air Force, Prof. Deutsch, and Mr. Brian Eastin for making these pdf files for us.

    Some remarks about Majorana and Dirac fields are available as a pdf file.

    Some solutions to the homework assignments are available as photocopies in the front office, room 100, and as the pdf files Problems 1.1.11 - 1.6.4 (and 2.5.13 - 2.5.22), Problems 1.7.6 - 2.4.15, Problems 2.5.13 - 2.11.3 and 3.2.2 - 3.2.16 and 8.3.4 - 8.3.8 and the extra-credit, Lie-algebra problem, and The solutions to the seventh set of homework problems -- thanks again to Capt. Babani.

  1. Fourth homework assignment: Do problems 2.5.(13,22,23); 2.9.13; 2.10.(8,11,15); and 2.11.(2,3). Also, compute the energy levels of a particle of mass m in an empty sphere of radius a. Also find the wave functions. Note that the wave functions must vanish at r = a. The definitions of the covariant derivatives of rank-2 tensors are given in the hint hint2-10-15.

  2. Fifth homework assignment: Do problems 3.1.2, 3.2.(2,7,9,13,14,15,16), 8.3.(4,6,8).
    Extra-credit problem.

  3. Sixth homework assignment: Do problems 3.3.12, 3.4.(7,9), 3.6.20,4.1.(1,3),4.3.(1,2), and also these special problems:

    1. Find the multiplication table for a group with three elements and prove that it is unique.
    2. Consider the 2 x 3 matrix A with elements
      ( 1 2 3)
      (-3 0 1).
      (A(1,1) = A(2,3) = 1, etc.) Perform the singular value decomposition
      A = U S V'
      where V' is the transpose of V. Find the singular values and the real matrices U and V.
    3. Consider the 6 x 9 matrix A with elements
      A(j,k) = x + x**j + i*(y - y**k)
      where x = 1.1 and y = 1.02 and * means multiplication while ** means exponentiation. Find the singular values, and the first left and right singular vectors. Lapack is one way to do this problem. This assignment is due on the Tuesday after Thanksgiving.

  4. Seventh homework assignment: Do problems 4.4.1, 5.1.1, 5.2.6, 5.6.1, 5.7.1, 6.1.1, 6.2.1, 6.2.4, 6.4.4. The homework is due at the time of the final exam. Problem session 3:30 pm on Wednesday, Dec. 17th, room 184.

    Physics 467

    Here is the 466 final exam. Students who got less than 100 on it must turn it in with all the answers as the first homework assignment of the course 467.

    The solutions to the first set of homework problems is available as the pdf file test1solutions

    Second homework assignment: Do problems 6.5.8, 6.7.1 (Just show that angles get multiplied by n.), 7.1.4a, 7.2.5, 7.2.7 (for a > |b| only), 7.2.14b, the problem assigned in class, to wit: the integral from -infinity to + infinity of (sin(kx)/x) dx for k<0 (You may use the result for k>0 derived in class.), and 7.2.16. Problem 7.2.18 was marred by a serious typo in the textbook.

    The solutions to the second set of homework problems is available as the pdf file HW2solutions

    Mammoth homework assignment: 14.1.(1, 3, 5, & 8); 14.2.2; 14.3.(4-7); and 14.4.(2 & 9-11).

    The solutions to the third set of homework problems is available as the pdf file HW3solutions

    Fourth homework assignment: Problems one and two were assigned in class; see pages 353--358. Also do exercises 15.3.(6,10,16), 15.4.(1,3,4), 8.2.14, 8.3.5, and 8.5.5.

    The solutions to the fourth set of homework problems is available as the pdf file HW4solutions

    Fifth homework assignment: 8.6.9, 8.6.15, 9.1.4, 9.2.5, 12.3.15, and 12.5.15.

    The solutions to the fifth set of homework problems is available as the pdf file HW5solutions

    By courtesy of Capt. Babani, the class notes are available as the pdf files: pages 228-252, pages 253-266, and 266-282, 283-303, 304-329, 330-336, 337-352, 353-363, 364-382, 383-397, 398-406, 407-419, 420-442, 443-457, and 458-463.