Here’s my chance to write about my own personal field, physics and computational physics! In this series we will be going over many subjects in both physics and computational techniques, including the Lagrangian formulation of classical mechanics, basic principles of quantum mechanics, the Path Integral formatulion of quantum mechanics, the Metropolis-Hastings Monte Carlo method, dealing with entropy and randomness in a pure language, and general principles in numerical computation! Fun stuff, right?
The end product will be a tool for deriving the ground state probability distribution of arbitrary quantum systems, which is somewhat of a big deal in any field that runs into quantum effects (which is basically every modern field). But the real goal will be to hopefully impart some insight that can be applied to broarder and more abstract applications. I am confident that these techniques can be applied to many problems in computation to great results.
I’m going to assume little to no knowledge in Physics and a somewhat intermediate working knowledge of programming. We’re going to be working in both my favorite imperative language and my favorite functional language.
In this first post I’m just going to go over the basics of the physics before we dive into the simulation. Here we go!