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n_(x)+n_(y-1),峰值个数为n_(x)·n_(y),且与Ψ=0平面的交线数也为n_(x)·n_(y);几率密度分布的极大值个数也为n_(x)·n_(y)。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。
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 n_(x)+n_(y-1),and the number of peaks is n_(x)·n_(y),and the intersection number of wave function and a plane of Ψ=0 is n_(x)·n_(y).The number of maximum of the probability density distribution also is n_(x)·n_(y),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.
作者
谢凯强
刘锴
吴坤
王茂隆
李玉洁
郑兴荣
XIE Kai-qiang;LIU Kai;WU Kun;WANG Mao-long;LI Yu-jie;ZHENG Xing-rong(College of Electrical Engineering,Longdong University,Qingyang,Gansu 745000,China)
出处
《井冈山大学学报（自然科学版）》
2021年第3期12-15,共4页
Journal of Jinggangshan University (Natural Science)
基金
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)。
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
two-dimensional potential box function
separated variable method
numerical simulation
wave function
probability density
energy
