• 教学讨论 •

### N 维势箱函数量子特性的可视化研究

1.  1. 陇东学院 电气工程学院 物理系，甘肃 庆阳 745000; 2. 西南大学 物理科学与技术学院，重庆 400715)
• 收稿日期:2021-05-21 修回日期:2021-06-27 出版日期:2022-01-20 发布日期:2022-01-13
• 作者简介:郑兴荣( 1986—) ，男，甘肃天水人，陇东学院电气工程学院物理系副教授，硕士，主要从事理论物理与材料物理的计算、仿真研究工作.
• 基金资助:
甘肃省青年科技基金( 20JR10RA135) ; 庆阳市自然科学基金项目( QY2021A-F014) ; 国家自然科学基金( 11565018) 资助

### Visualization research on the quantum properties of N-dimensional potential box functions

ZHENG Xing-rong¹，ZHENG Yan-fei²

1. 1. Department of Physics，College of Electrical Engineering，Longdong University，Qingyang，Gansu 745000，China; 2. School of Physics Science and Technology，Southwest University，Chongqing 400715，China
• Received:2021-05-21 Revised:2021-06-27 Online:2022-01-20 Published:2022-01-13

Abstract:

Using quantum theory derivation and numerical calculation methods，the diagram and model

of one- dimensional potential box function are firstly obtained. Then the wave function，energy

level and probability density of N-dimensional potential box functions in quantum mechanics are

studied comprehensively and systematically. Fi- nally，all characteristics of the potential box

functions are simulated using MATLAB software. We find that the ener- gy of particles is quantized

and discontinuous in N-dimensional potential box. The quantum number n cannot be ze- ro，and the

higher the quantum number n is，the higher the energy level is，while the higher the mass

m is，the lower the energy level is. Generally，the larger one-dimensional potential box length a

is，the lower the correspond- ing energy level is. The number of nodes is N-1，and the more

the nodes are，the shorter the wavelength is，the higher the frequency is，the higher the energy

level is. For two-dimensional potential box function，the number of peaks is nₓ ×ny ，and the

intersection numbers of wave function and a plane of Ψ = 0 is nₓ ×ny ，too. For degeneracy， in

general，the degeneracy of particles in the two-dimensional potential box model is uncertain. But

for the two di- mensional square potential box function model，the energy level degeneracy of the

particles in the box can be divid- ed into general and special cases. The degeneracy of

three-dimensional potential box function are nx +ny +nz . The vi- sualization results are in

complete agreement with the theoretical results. Finally，the color function of MATLAB

software is firstly used to realize the four-dimensional representation，and the four-dimensional

slice diagram of the three-dimensional potential box function are obtained. The results of

this visualization are in complete agreement with the theoretical results，and it is also of

great significance for the understanding of the abstract concept.