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American Journal of Physics

Monte Carlo image representation

Verissimo Manoel de Aquino, Valdir C. Aguilera-Navarro, Mário Goto, Hiromi Iwamoto

Published Jul 1, 2001• 4 citations
Publisher

Abstract

A simple method for representing probabilistic systems visually based on a Monte Carlo approach is discussed. Applications are given for the hydrogen atom and the propagation of wave functions associated with tunneling through a potential barrier.
DOI
10.1119/1.1339277

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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.
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