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

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。

According to the finite difference principle, a one-dimensional Schr6dinger 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.