PHGN 511
Mathematical Methods in Physics
Fall 2022

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.