Methods of Computational Quantum Mechanics (v 1.0)
Link to all the code in the book
- 1.1: Quantum mechanics: the bare minimum
- 1.2: The grid approach
- 1.3: Implementation in Python
- 1.4: Example: Kronig-Penney model
- 1.5: Basis functions
- 1.6: Kronig-Penney again
- 2.1: Density functional theory
- 2.2: The Kohn-Sham equation
- 2.3: Implementing a program
- 3.1: Density Functional Theory of Atoms
- 3.2: Solving the KS equation
- Afterword: Learning More
- 4: Solids?
Some time ago, I wrote an article that was somewhat well-received on the very basics of computational quantum mechanics. In that article, only non-interacting systems were considered.
Afterwards, I tried to write another article to get the reader closer to realistic, interacting systems. However, I sort of miscalculated: this article really doesn't work without reading the first, and these two articles were not really connected in a logical fashion. The material in this booklet starts from modified versions of two posts I've written on this site previously, but builds on it considerably.
It became obvious to me, then, that it was unrealistic to approach the goal of interacting systems in a piecemeal fashion through blog posts. It was, however, my hope to be able to provide a gentle introduction to interacting systems as well, since non-interacting systems alone aren't very interesting. I resolved, then, to instead write a booklet that contains a logical structure that you can follow along, with all the source code available online.
This page is the index of that book. If you want everything out of it, you should read it in a linear fashion, start to finish. It's only about ~60-70 pages long, with a fair bit of that being code, so it can probably be worked through in a couple of days.
I'm also considering writing a final chapter on full 3D calculations, but it's very much a work in progress.