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COURSE TIME:
Tuesdays and Thursdays 1:40 - 3:00 pm
COURSE LOCATION: Roessler 55
INSTRUCTOR:
Richard Scalettar
TEACHING ASSISTANTS:
Anandita De
TEACHING ASSISTANT:
Hanshang Jin
GRADING:
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TEXT:
None required. See below.
Homework assignments (due weekly on Fridays) will also contain
some numerical work. If the coding looks like it
will be too heavy, I will make those problems optional,
for extra credit. I plan to delay getting too
deep into numerical work
for a few weeks, so that I can take advantage
of material you will learn in Physics 102.
I have not selected a specific textbook. Most standard books
on mathematical physics
will have discussions of the material I present. I personally
like
"Mathematical Methods in the Physical Sciences",
by Mary Boas,
quite a bit. You will probably find a lot of useful initial material
for topics we will cover in your
second year calculus books, although we will likely go
a good deal further, and of course emphasize the physics
applications.
Course Outline (Tentative)
Problem Sets (Some of these are from 2016. They will be updated.)
Some Additional Fourier Problems (with Solutions)
Exams
Sample Exams
Grab Your Popcorn!
Course Objective:
The goal of this course is to familiarize you with the basic tools
of mathematical physics. I will mix traditional
exposition of textbook material with modern applications.
These will mostly be drawn from condensed matter physics, since
I am most familiar with the mathematical physics
which is useful for current research in that field.
As an example, when we discuss matrix diagonalization and eigenvalues,
we will see how this can be used to compute energy bands in solids,
and unusual features like flat bands, disorder localized modes,
the 'Dirac' spectrum of graphene, etc,
which are of interest in current research.
1. Complex Numbers
Lecture Notes
Connections to conservative Forces
1P. Functions of a Complex variable
Lecture Notes, Pt 1
Lecture Notes, Pt 2
Lecture Notes, Pt 3
Lecture Notes, Pt 4
2. Power Series; Taylor Expansion
Lecture Notes
3. Linear algebra (with applications to normal modes and quantum
mechanics)
Lecture Notes, Pt 1 (basic matrix
operations, special matrix types)
Lecture Notes, Pt 2 (more on special
matrix types, matrices in classical mechanics
Lecture Notes, Pt 3 (more on matrices in
classical mechanics- normal modes)
Lecture Notes, Pt 4 (more on matrices in
classical mechanics- normal modes)
Lecture Notes, Pt 5 (more on matrices in
classical mechanics- normal modes; projection matrices)
Lecture Notes, Pt 6 (triatomic molecule)
Lecture Notes, Pt 7 (vectors vs
components; operators vs matrices)
Lecture Notes, Pt 8 (energy bands in
solids)
Lecture Notes, Pt 9 (eigenvector
review)
Lecture Notes, Pt 10 (matrices in quantum
mechanics)
4. Vector spaces
Lecture Notes, Pt 1 (intro)
Lecture Notes, Pt 2 (example: the space
of differentiable functions; more theory)
Lecture Notes, Pt 3 (quantum mechanical
time evolution)
5. Fourier Series and Fourier Integrals
Lecture Notes, Pt 1 (general
theory)
Lecture Notes, Pt 2 (three applications:
qm of particle in box, wave equation, LRC circuit)
Lecture Notes, Pt 3 (application 4:
Laplace's Eqn; comments on numerics)
Life of Fourier (Lagrange and Laplace
unsatisfied...)
Lecture Notes, Pt 4 (Fourier
integrals; wave functions in position and momentum space; diffusion
equation)
X. Vector Calculus
Lecture Notes
6. Legendre Series
7. Partial Differential Equations: Integrated into previous lecture
materials
Assignment 1
Solutions
Assignment 2
Solutions
Assignment 3
Solutions
Assignment 4
Solutions
Assignment 5
Assignment 5B
Combined 5 and 5B Solutions
Assignment 6
Solutions to Problems 1,2 (and
one irrelevant problem)
Assignment SMOKE
Solutions
The Platters' "Smoke Gets in
Your Eyes"
Assignment 7
Solutions to problems 4 and 5
(and an irrelevant one)
Fall 2015 Problem Set 6 and Solutions
Fall 2018 Midterm Exam and Solutions
Fall 2015 Midterm Exam
Solutions
Fall 2015 Final Exam
Solutions
Fall 2016 Midterm Exam and Solutions
Fall 2016 Final Exam (no solutions)
My movie of Gaussian wave packett hitting a barrier
Anatoliy's movie of wavepacket spreading in a box
