Quantum Mechanics

The core of these notes were developed principally for a Quantum Mechanics class I taught, but like with the Classical Mechanics notes, they aggrandized over the years, and now there's way more than one could cover in a semester/year. So I broke it up into parts. Foundations deals with Hilbert Space stuff and the basic postulates. I spent some time being deliberate about going from a finite Hilbert Space to a continuous one, and also how to represent operators in a continuous Hilbert Space - things which always bothered me when I was a student. The treatment is of the same spirit as found in Sakurai. Time-Independent H's is concerned with solving for a bunch of eigenfunctions and energy levels. It includes approximate methods too (PT, WKB, Variational). Time-Dependent H's has pretty self-explanatory content. It covers the usual approximation method (PT), but I also spent time working out exact solutions: free particle, particle subject to constant force, and harmonic oscillator. I also decided to spend some time on Green's Functions - not that this is the place where they're most fruitful, but it's nice to see them in a simple context before getting serious about it when dealing with multiple particles, or fields. Scattering deals with, well, scattering. I do 1D and quasi-1D scattering (kind of like wave guides) more extensively than typical, because I wanted to be able to compare T-matrix and S-matrix results that we get in 3D to what we get in 1D, or quasi-1D. Then there is Multiple Particles. In the Distinct Particles section, I do stuff like a harmonic lattice, and also discuss GF's again. In the Identical Particles section I do Pauli-Exclusion, etc., and develop 2nd quantization, and Green's Functions in that context. The GF techniques studied here are all of the non-equilibrium variety since we haven't got to thermal averaging yet. Finally, Relativistic Quantum Mechanics covers its namesake, especially with an eye towards QFT.