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Academic Journal of Mathematical Sciences, 2023, 4(3); doi: 10.25236/AJMS.2023.040307.

Visualization and Analysis of Three-Dimensional Linear Harmonic Oscillator


Sihui Yan1, Jie Huang2

Corresponding Author:
Sihui Yan

1School of Physics and Material Science, Tianjin Normal University, Tianjin, 300000, China

2School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou, 511400, China


Quantum mechanics holds a very important position as the theoretical foundation of the micro world. Harmonic oscillator system is a very classical model in quantum mechanics. In this paper, the wave function of a three-dimensional linear harmonic oscillator is derived based on the linear harmonic oscillator model in quantum mechanics. According to the probabilistic interpretation of quantum mechanics, we obtain the probability density function of the harmonic oscillator electron cloud. In this paper, Monte Carlo selection method is used for sampling, and Mathematica software is used to draw electron cloud images with different quantum number, so that people can intuitively see the distribution of electron cloud in three-dimensional space.


Linear harmonic oscillator, Visualization, Monte Carlo simulation

Cite This Paper

Sihui Yan, Jie Huang. Visualization and Analysis of Three-Dimensional Linear Harmonic Oscillator. Academic Journal of Mathematical Sciences (2023) Vol. 4, Issue 3: 41-46. https://doi.org/10.25236/AJMS.2023.040307.


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