摘要
一维无限深势阱是量子力学中最基本且最简单的模型,其理论结果可以清晰地展示量子力学中的几率波和能量离散化等概念。但对于实际应用系统,当势阱从无限深势阱变成有限深势阱时,薛定谔方程的求解却并不简单,大部分的体系难以求出解析解,而需要解析法和数值法进行分析和讨论。作为一种有益的探索,本文成功将转移矩阵法(TM)应用于不含时薛定谔方程的求解。借助Matlab软件强大的计算功能,得到了粒子在一维有限深势阱中运动的能量本征值并绘制出了对应于不同势阱的波函数和位置分布概率图像,此举可加强学生对一维势阱模型的理解。
One-dimensional infinite potential well is the most basic and simple model in quantum mechanics.And Its theoretical results can clearly show the basic concepts in quantum theory such as the probability wave,energy discretization and so on.However,for the practical systems,when the depth of potential well is changed from infinite to finite,it is difficult to find the analytical solutions of Schrodinger equations,then different analytical methods and numerical methods are needed to discuss the characteristics of the quantum systems.As an exploration,the transfer matrix(TM)method is introduced to solve the time-independent Schrodinger equations in this paper.With the help of Matlab software,the energy eigenvalues of particles in different one-dimensional finite potential wells can be solved,as well as the wave functions and position distribution probabilities.These demoes can help students to understand the one-dimensional potential well model better.
作者
陈凤翔
曹功辉
汪礼胜
CHEN Fengxiang;CAO Gonghui;WANG Lisheng(Department of Physics Science and Technology, Wuhan University of Technology, Wuhan, Hubei 430070)
出处
《物理与工程》
2020年第2期37-43,48,共8页
Physics and Engineering
基金
武汉理工大学教学研究项目(w2016002和w2015053)资助。
关键词
转移矩阵法
一维有限深势阱
能量本征值
波函数
transfer matrix method
one-dimensional finite potential well
energy eigenvalue
wave function
