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

✍ Scribed by Houde Han; Jicheng Jin; Xiaonan Wu

Publisher
Elsevier Science
Year
2005
Tongue
English
Weight
820 KB
Volume
50
Category
Article
ISSN
0898-1221

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✦ Synopsis

A finite-difference scheme is proposed for the one-dimensional time-dependent SchrSdinger equation. We introduce an artificial boundary condition to reduce the originM problem into an initial-boundary value problem in a finite-computational domain, and then construct a finitedifference 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 numericM examples are given to show the effectiveness of the scheme. (~) 2005 Elsevier Ltd. All rights reserved.

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