快速傅里叶变换方法求解定态薛定谔方程  

Solution of the stationary Schr dinger equationby the fast Fourier transform method

作　　者：刘笑飞 张晓燕 方基宇 牛中明 LIU Xiao-fei;ZHANG Xiao-yan;FANG Ji-yu;NIU Zhong-ming(Stony Brook Institute at Auhui University,Anhui University,Hefei,Anhui 230039,China;School of Physics and Optoelectronic Engineering,Anhui University,Hefei,Anhui 230039,China;School of Mechanics and Photoelectric Physics,Anhui University of Science and Technology,Huainan,Anhui 232001,China)

机构地区：[1]安徽大学纽约石溪学院,安徽合肥230039 [2]安徽大学物理与光电工程学院,安徽合肥230601 [3]安徽理工大学力学与光电物理学院,安徽淮南232001

出　　处：《大学物理》2024年第11期23-25,31,共4页College Physics

基　　金：安徽省研究生教育教学改革研究项目(2022jyjxggyj130);安徽大学应用物理学专业教学团队项目(2022xjzlgc055);安徽大学《计算物理》研究生精品课程项目资助。

摘　　要：定态薛定谔方程通常在坐标空间使用有限差分法和打靶法等算法数值求解.本文采用傅里叶变换在动量空间数值求解定态薛定谔方程,借助快速傅里叶变换算法大幅提高了数值求解速度,并编写了相应的MATLAB数值程序.通过与一维谐振子本征值和本征波函数的解析解对比,验证了该方法的可靠性和数值程序的正确性,为定态薛定谔方程的求解提供了一种高效的数值算法.The stationary Schr dinger equation is usually solved numerically using the finite difference method and shooting method in the coordinate space.This paper employs the Fourier transform to numerically solve the stationary Schr dinger equation in the momentum space,the solving speed is greatly improved by using the fast Fourier transform algorithm, and the corresponding MATLAB numerical codes were developed. By comparing with the analytic solutions of the eigenvalues and eigenfunctions of the one-dimensional harmonic oscillator, the reliability of the method and the correctness of the codes are verified, which provides an efficient numerical algorithm for solving the stationary Schr dinger equation.

关 键 词：薛定谔方程 快速傅里叶变换 一维谐振子 

分 类 号：O4-39[理学—物理]