HydrogenAtom

MATLAB visual simulation of the Schrödinger equation of Hydrogen Atom

Introduction

这个程序组目的在于绘制各部分的氢原子模拟方程,包含球谐方程,径向方程,电子云模拟

The purpose of this set of programs is to plot the equations for the various parts of the hydrogen atom simulation, including the Spherical Harmonic, Radial Function and Hydrogen Electron Cloud.

Program

Guo_Spherical_harmonic.m

https://github.com/GuoYimingac/HydrogenAtom/blob/main/Guo_Spherical_harmonic.m

This function can be used to obtain an image of the spherical harmonic equation by entering the orbital quantum number, the magnitude quantum number, and optionally rotating and dragging it.

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Guo_Radial_function.m

https://github.com/GuoYimingac/HydrogenAtom/blob/main/Guo_Radial_function.m

This function is obtained by entering the principle quantum number and the orbital quantum number.The radial function (the horizontal coordinate is the ratio of the radius to the Bohr Radius)

The second image is that of the probability distribution of the radial distribution obtained by the Monte Carlo method.

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Peter_Electron_cloud.m

https://github.com/GuoYimingac/HydrogenAtom/blob/main/Peter_Electron_cloud.m

This function plots the isosurface graph with set probabilty of 0.5 by entering three quantum numbers.

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Monte Carlo.m

https://github.com/GuoYimingac/HydrogenAtom/blob/main/Monte_carlo.m

The test program for Monte Carlo method

LaguerreGen.m

https://github.com/GuoYimingac/HydrogenAtom/blob/main/LaguerreGen.m

Auxiliary program for solving legendre polynomials

How to use

Plot Spherical Harmonic:

<iframe width="806" height="504" src="https://www.youtube.com/embed/xo_ccJpUOzk" title="YouTube video player" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe>

Plot Radial Function:

<iframe width="806" height="504" src="https://www.youtube.com/embed/FeEqNSLN7kA" title="YouTube video player" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe>

Plot Electron Cloud:

<iframe width="790" height="494" src="https://www.youtube.com/embed/q7TJMceK_2c" title="YouTube video player" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe>

Reference:

1. Hydrogen Orbitals. https://www.mathworks.com/matlabcentral/fileexchange/64274-hydrogen-orbitals.
2. Bohr, N. I. On the constitution of atoms and molecules. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 26, 1–25 (1913).
3. Garcia, R., Zozulya, A. & Stickney, J. MATLAB codes for teaching quantum physics: Part 1. arXiv:0704.1622 [physics] (2007).
4. Monte Carlo method. Wikipedia (2021).
5. Szego, G. ORTHOGONAL POLYNOMIALS. 440 doi:10.1090/coll/023.
6. Spherical harmonics. Wikipedia (2021).
7. 刘浩 & 韩晶. MATLAB R2016a完全自学一本通. (2016).
8. MATLAB01:基本的数学运算与矩阵运算_ncepu_Chen的博客-CSDN博客. https://blog.csdn.net/ncepu_Chen/article/details/103034286.
9. MATLAB官方文档.
10. 曾谨言. 量子力学导论. (北京大学出版社, 1998).
11. Young, H. D., Freedman, R. A., Ford, A. L. & Sears, F. W. Sears and Zemansky’s university physics: with modern physics. (Pearson, 2016).
12. Griffiths, D. J., & Schroeter, D. F. (2018). Introduction to quantum mechanics. Cambridge University Press.