有限差分法求解薛定谔方程  

Solving the schr dinger equation by finite difference method

作　　者：乔鹏 方基宇 牛中明[1] QIAO Peng;FANG Ji-yu;NIU Zhong-ming(School of Physics and Materials Science,Anhui University,Hefei,Anhui,230601)

机构地区：[1]安徽大学物理与材料科学学院,安徽合肥230601

出　　处：《贵州师范学院学报》2019年第12期28-32,共5页Journal of Guizhou Education University

摘　　要：对于许多量子系统很难得到薛定谔方程解析解这个问题,提出采用有限差分法求解薛定谔方程,将连续的量子力学本征值问题转化为离散的本征值问题,给出了具体的数值计算公式,并编写相应的计算程序求解得到的矩阵方程。以一维和三维谐振子为例,讨论了其本征值和本征波函数的求解情况,借助相关软件对计算数据进行分析,通过与解析解进行对比,验证了有限差分法求解薛定谔方程的可行性与精准度。For many quantum systems,it is difficult to obtain the analytical solution of Schr dinger equation,the finite difference method is proposed to solve the Schr dinger equation,the continuous eigenvalue problem of quantum mechanics is transformed into the discrete eigenvalue problem,and the specific numerical calculation formula is given.In addition,writing the corresponding calculation program to solve the resulting matrix equation.With one-dimensional and three-dimensional harmonic oscillators as a case,the solution of its eigenvalue and eigenwave function is discussed.Finally,the feasibility and accuracy of the finite difference method to solve the schrodinger equation are verified by comparing the calculated data with the analytical solution.

关 键 词：有限差分法 薛定谔方程 本征值 本征波函数 

分 类 号：O411.1[理学—理论物理]