Probability image of electron in hydrogen by Matlab

Wei Shi

With an aim at the abstract conception of wave functions for hydrogen atom in quantum mechanics,this paper suggests the radial distribution,angular distribution and spatial distribution function of hydrogen atom electronic cloud,and also,Matlab software is used to plot their corresponding distribution charts.The analytical results indicate that the distribution patterns of hydrogen atom electronic clouds are co-determined by the radial and angular probability distribution,and that the electronic cloud distribution density is so uneven that the orbit trace can be observed.Accordingly,this method can reveal the radial,angular and spatial probability distribution laws of hydrogen atom electronic clouds intuitionally,whereby a new thinking way for analyzing the abstract wave function visualization in quantum mechanics is provided in this paper.

Nikom Choosiri, Virulh Sa-yakanit

Xijin Fu

Abstract Based on the theory of quantum mechanics, this paper systematically analyzes the basic characteristics of n-dimensional linear harmonic oscillator in quantum mechanics, focuses on the eigenfunction and probability density of one-dimensional harmonic oscillator, and simulates the eigenfunction and probability density of some energy levels with MATLAB software. Finally, MATLAB software was used to compare the probability distribution of linear harmonic oscillator in classical mechanics and quantum mechanics. The results indicate that the number of points of intersection between a wave function and a φ=0 line is n; The probability distribution satisfies the normalization condition; Taking different values of n, the probability distribution function of harmonic oscillator in quantum mechanics has n different nodes, and the amplitude of harmonic oscillator in classical mechanics also changes accordingly. φ0 by the ground state probability distribution of quantum mechanics and classical mechanics distribution probability of the simulation image can be seen that the shape of the two distribution curve is the opposite, but when n is large, the probability density of quantum mechanics |ϕn (ξ)|2 local average and classical probability distribution P(ξ), that is, classical mechanics and quantum mechanics ZhongZhen gradually increase the probability distribution of similarity. These results are reflected in the image, and the characteristics shown in the image are consistent with the theoretical results.

Sameer Krishna, Pratham Maliya

Wenying Xu

Quantum mechanism is a more Abstract science.In order to display some principles and experimental results in quantum mechanics with a more intuitive way,the MATLAB software is used to build a visual platform for quantum mechanics,which can vividly demonstrate double-slit electron diffraction,quantum tunneling effects,the hydrogen atoms electron cloud and the Stark effect and so on.When the related physical parameters are inputted,the corresponding physical phenomena will display on the platform,which allow the students to obtain a more direct learning experience in study.