A finite-difference method for the one-dimensional time-dependent Schrodinger equation on unbounded domain

被引：43
作者：
Han, HD
Jin, JC [1 ]
Wu, XN
机构：
[1] Tsing Hua Univ, Dept Math Sci, Beijing 100084, Peoples R China
[2] Xiangtan Univ, Dept Math, Hunan, Peoples R China
[3] Hong Kong Baptist Univ, Dept Math, Kowloon, Hong Kong, Peoples R China
来源：
COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2005年 / 50卷 / 8-9期
关键词：
the Schrodinger equation; finite-difference method; artificial boundary conditions;
D O I：
10.1016/j.camwa.2005.05.006
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A finite-difference scheme is proposed for the one-dimensional time-dependent Schrodinger equation. We introduce an artificial boundary condition to reduce the original problem into an initial-boundary value problem in a finite-computational domain, and then construct a finite-difference scheme by the method of reduction of order to solve this reduced problem. This scheme has been proved to be uniquely solvable, unconditionally stable, and convergent. Some numerical examples are given to show the effectiveness of the scheme. (c) 2005 Elsevier Ltd. All rights reserved.
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页码：1345 / 1362
页数：18
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