Monte Carlo method to explain the probabilistic interpretation of atomic quantum mechanics

Abstract

ABSTRACTQuantum mechanics description of physical and chemical systems is included in books of Physics, General Chemistry or Physical Chemistry including mathematical, graphical, and conceptual descriptions. Mathematical calculations are complex and are covered only in advanced courses. Main problem in the first degree courses is the understanding of the probabilistic interpretation of quantum mechanics. The Monte Carlo method is based on probabilistic concepts and its application to quantum calculations can be carried out quite straightforward. In this work, a simple Monte Carlo method was used to obtain a sequence of random electron coordinates according to the probability given by the wave function. Electron is seen as a shot whose appearance is only accepted and plotted when probability is high enough. Hydrogen atom was studied as it is a familiar system for most students and its description can be easily related to previous knowledge of atomic orbitals. The objective of the present work is to supply all the crucial points that students need to create their own program to plot atomic orbitals according to the above ideas. All the numerical details are indicated in order to get the proposed programming project as a simple task. Student should be able to generate random electron coordinates, to compute wave functions and probabilities, and to obtain plots according to the right probabilistic interpretation of quantum mechanics. In order to show the quantitative obtained plots some results were shown. Typical s, p, and d orbitals were obtained and compared to the usual angular and radial representation. © 2016 Wiley Periodicals, Inc. Comput Appl Eng Educ 24:765–774, 2016; View this article online at wileyonlinelibrary.com/journal/cae; DOI 10.1002/cae.21749