Mathematical Methods in Physics
PHGN 511 Mathematical Methods in Physics Fall 2022
The Facts:
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- Me: Alex Flournoy aflourno@mines.edu and my fill in Laith Haddad lhaddad@mines.edu
- Lecture: T/TR 5:15-6:30pm in CK150
- Required text: "Mathematics of Classical and Quantum Physics" by Frederick Byron and Robert Fuller.
- Office Hours: Wednesdays from 5-7:50pm via Zoom.
- Evaluation: Your grade will be based on lecture participation (10%), homework (40%), an in-class midterm exam (20%) and a takehome final exam (30%).
Lecture participation will be assessed by your response to questions posed during lecture. I will draw names randomly to answer questions and if you are not present or fail to respond as if paying attention, you will lose 1% of the 10% for lecture participation. Any student sitting in on the course (not enrolled) will be expected to take part in lecture participation or asked to refrain from attending.
Homework will be assigned regularly and "due" on Thursdays. Instead of turning in your assignments I will administer short homework quizzes.
The quiz will consist of two questions from which you will choose one to answer. Each question will be very similar to a part of one of the homework problems, but not identical.
You will be allowed to use your homework solutions to help you on the quiz, but not your book. If you are a good then perhaps you will be able to work the quiz problems on the fly, but with the time constraint this will be next-to-impossible for most, so you should try your best to complete the assignments on your own. The reasons for this are two-fold. First it cuts out the motivation for simply copying someone else's homework, and secondly it will make the grading more expedient.
Description:
This is the newest version of this course. Originally it was taught in conjunction with graduate Classical Mechanics. As of this semster, we no longer require Classical Mechanics as a requirement. This was chosen to free up students time and energy for a lab course. Of course this meant that the important ideas from Classical Mechanics must appear somewhere. So some of it will appear here, at the expense of some items covered before.
Objectives:
Our goal will be to start with a more mathematical analysis of vector spaces, beginning with the finite dimensional cases (applying the results to space and spacetime), then moving onto the infinite-dimensional cases (applying the results to quantum mechanics). Topics among these include abstract definitions and theorems, the idea of bases, transformations, inner-products, and classifications of operators and their properties. We will then move onto analytic function theory, and study the power of complex variables. After that we will look at solutions generating techniques such as Green's functions and perturbation theory. In the end (or perhaps earlier) we will go over aspects of group theory as applied to physics. To get started, we will employ the mathematical language wherein we distinguish definitions (not to be proven) from theorems (which must be proven). This mathematical rigidity will accompany us for a while, but eventually we will disband of it and use physics language most of the time.
Lectures:
I will point out relevant sections of the suggested text for further reading. After each lecture, I will post my notes below as well.
Homework:
Exams: