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Journal of Huaibei Industry Teachers College

Plotting Spatial Distribution of Wave Function of Hydrogen Atom in Matlab

Jian Liu

Published Jan 1, 2004• 0 citations
OpenAlex

Abstract

In consideration of the abstract characteristics of wave function ofhydrogen atom in quantum mechanics, making use of the MATLAB to plot spatial distribution,pointing out the software of MATLAB is a valid tool to visualization of quantum mechanics.

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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.
This study conducted a detailed study on the wave function characteristics of the hydrogen atom model and explored its potential applications in quantum computing, atomic spectral analysis and quantum information processing based on the Schrödinger equation. By solving the Schrödinger equation of the hydrogen atom, the form of the wave function was clearly obtained, and the distribution law of electrons at various energy levels was demonstrated. The study constructed a quantum theoretical model of the hydrogen atom, derived the regulatory effect of quantum numbers on the wave function, and solved the Schrödinger equation with the help of numerical analysis technology to ensure the accuracy and robustness of the wave function evaluation. The study conducted a detailed analysis of the energy level, wave function profile and electron probability density distribution of the hydrogen atom. The simulation results show that with the increase of energy level, the oscillation frequency of the wave function increases significantly, and the distribution space of electrons also expands accordingly. In addition, this study also explored the practical application of the hydrogen atom model. In the field of quantum computing, the wave function characteristics provide theoretical support for the initialization and manipulation of quantum bits; in atomic spectral analysis, accurately calculated energy levels and wave functions help to improve the accuracy of spectral measurement; in quantum information processing, the simulation of quantum entangled networks based on the hydrogen atom model provides new ideas for quantum communication and quantum computing. These applications demonstrate that the hydrogen atom model is not only of great significance in theoretical physics, but also has broad application prospects in emerging technology fields.
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.
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.