红外, 2010, 31 (3): 42, 网络出版: 2011-02-23
通过有限差分和MATLAB矩阵运算直接求解一维薛定谔方程
Direct Solution of One-dimensional Schr dinger Equation through Finite Difference and MATLAB Matrix Computation
半导体 量子力学 薛定谔方程 有限差分法 semiconductor quantum mechanics Schr?dinger equation finite difference method MATLAB MATLAB
摘要
根据有限差分法原理,将求解范围划分为一系列等间距的离散节点后,一维薛定谔方程转化为可以用一个矩 阵方程表示的节点线性方程组。利用MATLAB提供的矩阵左除命令,即可得到各未知节点的函数近似值。该方法概念简单,使用方便, 不需要花费较多精力编程即可求解大型线性方程组。
Abstract
According to the finite difference principle, a one-dimensional Schr?dinger equation can be converted into a set of nodal linear equations expressed in a matrix equation after the space is divided into a series of discrete nodes with an equal interval. The matrix left division command offered in the MATLAB software can be used to derive the function approximation of each unknown nodal function. This method is simple in concept, convenient in operation and can solve large linear equations without more efforts in programming.
参考文献
[1] 王忆锋, 毛京湘. 用MATLAB实现普朗克函数积分的快捷计算 [J]. 红外, 2008, 29(4): 12-14.
[2] 王忆锋, 毛京湘. 用MATLAB和数值逼近方法实现费米函数的简捷计算 [J]. 红外, 2008, 29(8): 34-36.
[3] 王忆锋, 毛京湘. 用MATLAB和打靶法实现平面PN结一维泊松方程的简捷计算 [J]. 红外, 2010, 31(2):446.
[4] 任玉杰. 数值分析及其MATLAB实现 [M]. 北京: 高等教育出版社, 2007.
[5] E B Magrab, S Azarm, B Balachandran等著. 高会生, 李新叶, 胡智奇, 等译. MATLAB原理与工程应用 [M]. 北京: 电子工业出版社, 2002.
[6] Tao Pang. An Introduction to Computational Physics [M]. Cambridge University Press, 1997.
王忆锋, 唐利斌. 通过有限差分和MATLAB矩阵运算直接求解一维薛定谔方程[J]. 红外, 2010, 31(3): 42. WANG Yi-feng, TANG Li-bin. Direct Solution of One-dimensional Schr dinger Equation through Finite Difference and MATLAB Matrix Computation[J]. INFRARED, 2010, 31(3): 42.