A smooth path to plot hydrogen atom via Monte Carlo method.

Abstract

In this paper, we show how to build a basic computer program using the Monte Carlo method to display the hydrogen atomic orbitals. For this, in a heuristic way, we applied a von Neumann acceptance-rejection method in simple problems of potential wells, and we end with the hydrogen orbitals representation. In this technique, we spread points uniformly on the 1D and 2D charts of probability density distributions, then we filtered points under these “curves or surfaces”, and we extended this logic to 3D cases. Throughout the work, we also made some comments to help beginner students better understand the term “wave function” present in the Schrödinger equation. Also, we made all source code available at a third-party platform, for any purpose under the MIT license. Keywords: hydrogen atom, quantum mechanics, Monte Carlo method, Neumann acceptance-rejection method.