Classes are over for the semester, and I’ve put together the lecture notes for my undergraduate “Quantum Mechanics for Mathematicians” course, which are available here.
The idea for the course was to try and explain the basics of quantum mechanics, from the point of view of unitary representations of Lie groups. While this is a rather advanced topic, I made an effort to do things quite concretely and start at the most basic level (the only prerequisite for the course was calculus and linear algebra). I hope the notes will be useful both to mathematicians trying to learn something about quantum mechanics as well as to physicists who would like to better understand the mathematics behind the way symmetry principles get used in the subject.
More to come next semester. The initial plan is to start with the fermionic oscillator, move on to path integrals, then relativity, the Dirac equation, and U(1) gauge theory (E and M), ending up with some very basic quantum field theory (non-interacting fields). We’ll see how that turns out and at what point I run out of energy and stop writing.
Any corrections, comments or suggestions about how to improve these notes are most welcome.
Update: Thanks to all for comments, I’m quite pleased to see how many people have been looking at these notes (6600 downloads and counting!). They’ve also made an appearance in surprising places, including here.