Physics 410       Math Methods in Physics      Fall 2007 News  |  Schedule  |   Description   |
Lectures: Text: Instructor: Raymond Frey , Wil 405, 346-5873, rayfrey@uoregon.edu MW 2:00-3:20, Wil 318 Office hours: Mon 11-12:30, Fri 2-3 Arfken and Weber,  Mathematical Methods for Physicists, 6th Ed. Vector calculus, ordinary differential equations. (Check with Prof Frey if questions.) http://physics.uoregon.edu/~rayfrey/410/   (this page) Midterm Exam (25%), Homework (40%), Final Exam (35%) Other Resources: Homework Solutions - links to pdf  files in table below

News/Announcements:
 Date Dec 4 Final exam solutions Dec 1 Final exam practice solutions.   (Note that all of the homework solutions and summaries are available from links below.) Dec 1 Office hours during finals week:  Mon: 9:30-11:30, 1:30-3:30;  Tues: 10-noon. Nov 30 Final exam practice problems  (Note: there is a type on problem 4.) Oct 29 Midterm solutions Oct 20 HW #4 posted below Oct 18 Practice Midterm Exam:  exam  |   solutions Oct 18 links to all HW solutions in table below Oct 17 Midterm exam is Monday Oct 22.  No class Weds Oct 24.  We will make up this class on Fri  Nov 30 at 2:00-3:20 Oct 9 short summaries for weeks 1-3

Lecture/Homework/Exam Schedule (to be updated continuously):
 Week Lecture Topic(s) Text  Chs. Homework ("Problems" from text ) HW Due Comment Sep 24 Orientation, goals. Review of some vector material. Finite linear spaces: matrices and matrix equations. Summary page. 3 #1:  3.1.1 , 3.1.2; 3.2.3, 3.2.20, 3.2.32, 3.2.34, 3.2.36; 3.3.9 10/1, in class HW1 Solutions Oct 1 Similarity transformations; hermitian and unitary operators; eigenvalue problems Summary page 3 #2:  3.3.12, 3.3.13; 3.4.3, 3.4.6, 3.4.12; 3.5.6, 3.5.8, 3.5.12, 3.5.20;  3.6.9 10/10 (W), in class HW2 Solutions Oct 8 hermitian operators, unitary transformations, and eigenvalue problems (contd) Summary page 3 #3: 3.5.9, 3.6.20; 1.15.1, 1.15.6, 1.15.9; 9.7.6, 10.1.1 10/18 by 5PM, or 10/17 in class HW3 Solutions Oct 15 Dirac delta fn (Ch 1.15);  overview of 2nd order ODE (Ch 9); Green's fns I (Ch 9.7); Sturm-Liouville systems intro Summary pages 1.15, skim 9; 10.1,10.2 #4: 10.1.8, 10.1.13, 10.1.16, 10.1.17; 10.2.5, 10.2.6 11/1 (Th) HW4 Solution Oct 29 Sturm-Liouville systems, Hermitian operators Summary pages 10.1,10.2 #5: 10.4.4; 12.3.2, 12.3.5; 14.3.4, 14.3.12, 14.3.14 11/9 HW5 Solutions Nov 5 generalized Fourier series, completeness Summary pages 10.4 10.5 12.3,14.3 #6:  10.1.11a, 10.2.3, 10.5.12; 15.3.5, 15.3.9, 15.3.16, 15.5.5, 9.7.16 11/21 HW6 Solutions Nov 12 Green's fns II (brief); Fourier transforms; transformation of differental equations; convolution; transfer fns Summary pages 15,1-15.7 Nov 19 contour integration (brief) Summary pages for contour integration 6.4,6.5,6.6 7.1 #7: 15.3.4, 15.3.10,  15.4.3, 15.6.8, 15.6.12 11/30 5 PM HW7 Solutions Nov 26 countour integ., Fourier transform applications (contd); Summary review Dec 4, Tue 15:15-17:15 Final Exam, Wil 318

Course Description and Plan (approximate):

The primary goal of the course is provide the mathenatical background necessary for a 400-level course in quantum mechanics.
We will start by covering linear algebra of finite spaces (mostly Ch 3 of the text).
We will then move to the heart of the course: Ch 10 of the text, from which we see how a certain class of differential equations are connected to the infinite function spaces commonly used in QM and other subjects.
We will look at some of the corresponding special functions, but will focus more on a familiar example -- Fourier series -- and then generalize this to the Fourier transform and look briefly at other integral transforms.
Details are below. The exact course plan and material will depend somewhat on student background and interest.

Summary notes written by Prof Frey will be provided.

Main topics to be covered:

• Linear algebra of vector spaces: ordinary and function
• Linear operators and their properties
• Sturm-Liouville systems
• Eigenvalue equations
• Inhomeogeneous differential eqns. and Green's functions
• Fourier series: standard and generalized
• Integral Transforms, esp. Fourier transforms and properties
• Possible additional/alternative topics: Cauchy's thm and contour integration
Approximate Course outline:
• Matrices and Linear Algebra of Vector Spaces (Text Ch 3)
1. Systems of equations; matrix inversion
2. Dirac notation
3. Operator properties; Hermitian and unitary matrices
4. Eigenvalue problems; matrix diagonalization
5. applications: principal axes, normal modes; Heisenberg vs Schrodinger
• Overview of Partial Differential Eqns. (Text Ch 9)
1. Some well-known equations
2. Dirac delta function (Ch 1)
3. Green's function overview
• Sturm-Liouville and related topics (text Ch 10)
1. Eigenvalue problems and Hermitian operators
2. vector spaces of orthogonal eigenfunctions
3. completeness
• Fourier series analysis and properties (text 14.1-14.4
• Fourier transform and properties (text 15.1-15.7)
1. inversion; application to differential equations
2. convolution
3. configuration/momentum representations in QM

Homework:

• Weekly homework will be posted above.
• Students are required to show their work and reasoning as appropriate to receive full credit. A model solution will be posted in week one.
• You are welcome to work on the homework with your classmates, and please feel free to seek help from me.
• Complete solutions will be available from this web site soon after the due date. Please refer to these.
Exams:

There will be one midterms and one final exam. Exams will be closed book, but the generally useful equations and information will be provided.
Practice exams and solutions will be provided approximately one week before an exam.