文章基本信息

标题：A Generalized FDTD Method with Absorbing Boundary Condition for Solving a Time-Dependent Linear Schrodinger Equation
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作者：Frederick Ira Moxley III ; Fei Zhu ; Weizhong Dai 等
期刊名称：American Journal of Computational Mathematics
印刷版ISSN：2161-1203
电子版ISSN：2161-1211
出版年度：2012
卷号：2
期号：3
页码：163-172
DOI：10.4236/ajcm.2012.23022
出版社：Scientific Research Publishing
摘要：The Finite-Difference Time-Domain (FDTD) method is a well-known technique for the analysis of quantum devices. It solves a discretized Schr?dinger equation in an iterative process. However, the method provides only a second-order accurate numerical solution and requires that the spatial grid size and time step should satisfy a very restricted condition in order to prevent the numerical solution from diverging. In this article, we present a generalized FDTD method with absorbing boundary condition for solving the one-dimensional (1D) time-dependent Schr?dinger equation and obtain a more relaxed condition for stability. The generalized FDTD scheme is tested by simulating a particle moving in free space and then hitting an energy potential. Numerical results coincide with those obtained based on the theoretical analysis.
关键词：Schrodinger Equation; Absorbing Boundary; FDTD Method; Stability