Modern physics and computational techniques: how to "see" the hydrogen atom

Abstract

This paper aims to bridge two subjects that have received increased attention in the final years of the basic education and the first years of undergrad education in science and technology areas: a bridge between an introduction to modern physics and an introduction to computer programming. As an example, the paper describes how to produce figures that represent, as a point density diagram or a color-coded diagram, the probability density for an electron in the hydrogen atom. This is accomplished through a short introduction to the basic physics of the problem and through detailed comments on algorithms that (a) implement the equations of the problem, (b) allow to generate random values from an arbitrary probability distribution and (c) effectively produce the figures. The main goal is to show the reader how modeling and visualization techniques are implemented using a subject that, in principle, is of her/his interest. The implementation uses HTML/CSS/JavaScript, an extremely versatile and accessible technology that underlays almost all internet content nowadays, including many education platforms.