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A Study of the Particle Probability Distribution by Using the Mathematica

Jiang Jun-qin

Published Jan 1, 2008• 0 citations
OpenAlex

Abstract

Two representative examples of the particle probability distribution are studied by using the Mathematica.The movement of the probability distribution of a superposition state from the two-dimensional harmonic oscillator is shown.A general method of drawing three-dimensional image for the electron probability angle distribution in the hydrogen atom is given;and a mistake from a textbook is corrected.

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Two representative examples of the particle probability distribution are studied by using the Mathematica.The movement of the probability distribution of a superposition state from the two-dimensional harmonic oscillator is shown.A general method of drawing three-dimensional image for the electron probability angle distribution in the hydrogen atom is given;and a mistake from a textbook is corrected.
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While in the process of studying hydrogen atom wave function in quantum mechanics course,some frequently-asked questions about the radial probability distribution,tree-dimensional angular distribution,and movement trace are raised by beginners.The visualized interpretations for those questions are made by the three dimension model set up in computer,which can not only help students to establish the correct quantum images about the movement of the particles,but also provide a reference for visualization about other quantum phenomena.
The Bohr model is highly successful in explaining many features of the hydrogen atom. The ground state wave function does not have any angular dependence. The normalized hydrogen atom wave functions are directly accessible in Mathematica and can be readily verified as solutions of the Schrodinger equation. Get the hydrogen atom ground state wave function in terms of the Bohr radius a. The probability of finding the electron per volume at a given location is given by the square of the wave function. The electron has only a very tiny probability of being found inside the proton, whose size is about 1 fm.