| 谢凯强,刘锴,吴坤,王茂隆,李玉洁,郑兴荣.二维势箱函数的可视化研究[J].井冈山大学自然版,2021,42(3):12-15 |
| 二维势箱函数的可视化研究 |
| VISUALIZATION RESEARCH OF TWO-DIMENSIONAL POTENTIAL BOX FUNCTIONS |
| 投稿时间：2020-12-11 修订日期：2021-02-06 |
| DOI：10.3669/j.issn.1674-8085.2021.03.003 |
| 中文关键词: 二维势箱函数 分离变量法 数值仿真 波函数 几率密度 能量 |
| 英文关键词: two-dimensional potential box function separated variable method numerical simulation wave function probability density energy |
| 基金项目:国家自然科学基金项目（11565018）；甘肃省青年科技基金项目（20JR10RA135）；甘肃省教育厅高等学校创新能力项目（2019A-112） |
| 作者 | 单位 | | 谢凯强 | 陇东学院电气工程学院物理系, 甘肃, 庆阳 745000 | | 刘锴 | 陇东学院电气工程学院物理系, 甘肃, 庆阳 745000 | | 吴坤 | 陇东学院电气工程学院物理系, 甘肃, 庆阳 745000 | | 王茂隆 | 陇东学院电气工程学院物理系, 甘肃, 庆阳 745000 | | 李玉洁 | 陇东学院电气工程学院物理系, 甘肃, 庆阳 745000 | | 郑兴荣 | 陇东学院电气工程学院物理系, 甘肃, 庆阳 745000 |
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| 中文摘要: |
| 运用分离变量法和数值仿真，得到了量子理论中二维势箱函数波函数及其相关特性的理论和可视化结果。结果表明：二维势箱函数的能级是量子化的；能量随着量子数的增加而增加，但势箱长度和宽度越大，能量越小。对于二维的正方势箱函数，粒子波函数的简并度为nx+ny-1，峰值个数为nx·ny，且与Ψ=0平面的交线数也为nx·ny；几率密度分布的极大值个数也为nx·ny。本文的这种推导结果和可视化结果与理论结果完全一致。通过可视化结果解决了势箱函数教学和科学研究的难题，并为用MATLAB数值计算解决同类问题提供借鉴。这对于抽象性概念的理解具有重要意义。 |
| 英文摘要: |
| Using the separated variable method and numerical simulation, the theoretical and visual results of the wave function and related properties of two-dimensional potential box function in quantum theory are obtained. The results show that the energy of particles is quantized in two-dimensional potential box. The energy increases with the quantum number, while decreases with the potential box length and width. For the square potential box function in two dimensions, the degeneracy of wave function is nx+ny-1, and the number of peaks is nx•n, and the intersection number of wave function and a plane of Ψ=0 is nx•ny. The number of maximum of the probability density distribution also is nx•ny, too. The results of the derivation and visualization in this paper are completely consistent with the theoretical results. The visualization results solve the difficult problems in teaching and scientific research of potential box function, and provide reference for solving similar problems with the numerical calculation MATLAB software. It is very significant for abstract concept to understand. |
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