傅里叶变换法求解两类简单的薛定谔方程

Solution of two simple Schr?dinger equations by Fourier transform method

自由粒子和一维无限深势阱的薛定谔方程的求解是量子力学较为基础的内容.本文采用傅里叶变换对这两类简单的薛定谔方程进行了求解讨论.通过偏微分方程的傅里叶变换解法和偏微分方程作分离变数成常微分方程后的傅里叶变换解法的深入讨论,均得到与有关教材一致的结果,并讨论了这两种方法之间的差别和联系.

The solution of Schr dinger equation for free particle and one-dimensional infinite potential well is the basic content of quantum mechanics.In this paper,Fourier transform is used to solve these two simpleSchr dinger equations.Through the in-depth discussion of the Fourier transform method of partial differential equation and the Fourier transform method of ordinary differential equation which separates from the partial differential equation by separated variable method,the results are consistent with those of relevant textbooks,and the differences and relations between the two methods are discussed.