Physics 452 Winter 2004
Methods of Theoretical Physics II


Instructor: Prof. James Wells (jwells@umich.edu)
Office: 3440 Randall Lab, 763-4478
Lectures: 2:40-4:00 MW in 1096 East Hall
Office Hours: 2:30-3:45 Tues/Thur
 
Grader: Meng Cui (mcui@umich.edu)
Office: 1485A Randall, 764-9578
 


Lectures and Homework

1. Wed Jan 7 §1. Laplace Transforms
2. Mon Jan 12 §2. Solving Differential Equations using Laplace Transforms
3. Wed Jan 14 §3. Two Important Properties of the Laplace Transform
§4. Laplace Transforms of Discontinuous Functions [ HW1 due]
X. Mon Jan 19 No Class -- MLK Day
4. Wed Jan 21 §5. The Dirac Delta Function
§6. Differential Equations with Dirac Delta Functions [ HW2 due]
5. Mon Jan 26 §7. Inverse Laplace Transform by Bromwich Integral
§8. Convolution Integrals
6. Wed Jan 28 §9. Green's Function and Poisson's Equation
§10. Symmetry of Green's Function and Self-Adjoint Linear Differential Equations [ HW3 due]
7. Mon Feb 2 §11. Quantum Mechanical Scattering Green's Functions
8. Wed Feb 4 §12. Numerical Solutions to Differential Equations [ HW4 due]
9. Mon Feb 9 §1. Basic Properties of Groups
10. Wed Feb 11 §2. The Group Rearrangement Theorem [ HW5 ]
11. Mon Feb 16 §3. Subgroups
§4. Equivalence Relations, Conjugate Elements and Conjugacy Classes
12. Wed Feb 18 Midterm in 445 Dennison (HW5 due)
X. Mon Feb 23 No Class -- Spring Break
X. Wed Feb 25 No Class -- Spring Break
13. Mon Mar 1 §5. Invariant Subgroups
§6. Cosets of Subgroups
14. Wed Mar 3 §7. Factor Groups from Cosets of Invariant Subgroups
§8. Homomorphic and Isomorphic Mappings [ HW6 due]
15. Mon Mar 8 §9. Direct Product and Semi-direct Product Groups
16. Wed Mar 10 §10. Permutation Groups
§11. Cayley's Theorem [ HW7 due]
17. Mon Mar 15 §12. Definition of a Group Representation
§13. Principal Theorems of Finite Group Representations
18. Wed Mar 17 §14. Representation Theory for Dihedral D4 Group [ HW8 due]
19. Mon Mar 22 §15. Group Theory and Vibrational Normal Modes
20. Wed Mar 24 §16. Normal Modes of the Water Molecule [ HW9 due]
21. Mon Mar 29 §1. Lie Groups of Unitary and Orthogonal Matrices
22. Wed Mar 31 §2. Lie Groups from Metrics on an Inner Product Space
23. Mon Apr 5 §3. The Lorentz Group [ HW10 due]
24. Wed Apr 7 §4. A Formal Definition of Linear Lie Group
§5. Connected Components of a Lie Group
25. Mon Apr 12 §6. Compact and Non-Compact Lie Groups
§7. Generators of Lie Groups
26. Wed Apr 14 §8. Lie Algebras [ HW11 due]
27. Mon Apr 19 §9. Lost Generators, Goldstone Bosons and the Eightfold Way
§10. Quantum Mechanics and Group Theory
28. Wed Apr 21 §11. Representations of the Schroedinger Equation Group
§12. Representation Theory and the Hydrogen Atom [ HW12 due]


Final Exam is Wed Apr 28 from 10:30am - 12:30pm (445 Dennison)


Physics Plan

Recommended Reference Textbook: Arfken/Weber,
Mathematical Methods for Physicists, 5th ed.

This semester course will be broken into three roughly
equal length mini-courses:

"Advanced Methods for Solving Differential Equations"
"Finite Groups"
"Lie Algebras"



Grade Evaluation

Total of 100 points possible in course.
50 points awarded for perfect Homework.
25 points awarded for perfect Midterm.
25 points awarded for perfect Final.

90 points or higher guarantees an A grade.
80 points or higher guarantees a B grade.
70 points or higher guarantees a C grade.
I might be more generous than this if warranted,
but the above scale is guaranteed.

All HW problems will be graded on the "3-point scale"
(aka, "the check plus minus scale"):
3 - correct and excellent showing,
2 - not correct but very good showing,
1 - weak showing (correct answer or not),
0 - no showing

Homework details: Homework is due at the beginning of class on
listed due date. Late homework is allowed up to the beginning of the next
class meeting, but the score will be halved. No homework will be accepted
after that. All homework will be counted. Petitioning for excused homework
must be made in writing to me no later than one week after the due date. I
generally do not excuse missed homework unless there is a very significant
reason (death in the family, sickness requiring doctor's care, etc.).

Midterm details: Midterm will cover first mini-course on differential
equations. This is sections §1 through §12 of our course. The exam will be
in 445 Dennison from 2:40-4:00 on Wed Feb 18. It is closed book except
students are allowed to bring in one 3x5 inch index card hand-written on both sides.

Final Exam details: The Final will cover the second and third
mini-courses on Finite Groups and Lie Groups. The exam will
be in 445 Dennison from 10:30-12:30 on Wed Apr 28. It is closed
book and notes except students are allowed to bring in one 3x5 inch
index card hand-written on both sides.


Additional Document Links


World of Mathematics
Undergraduate Research Opportunities (Dept)
Undergrad Research (MCTP)
Principal Theorems of Finite Group Representations