Physics 410       Math Methods in Physics      Fall 2007
Liouville HilbertHeisenberg
News  |  Schedule  |   Description   |

Instructor:
Raymond Frey , Wil 405, 346-5873, rayfrey@uoregon.edu
Lectures: MW 2:00-3:20, Wil 318
Office hours: Mon 11-12:30, Fri 2-3
Text:  Arfken and Weber,  Mathematical Methods for Physicists, 6th Ed
Pre-requisite: Vector calculus, ordinary differential equations. (Check with Prof Frey if questions.)
WWW: http://physics.uoregon.edu/~rayfrey/410/   (this page)
Grading: 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:

Approximate Course outline:

Homework:

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.



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