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

Houde Han; Jicheng Jin; Xiaonan Wu

doi:10.1016/j.camwa.2005.05.006

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

Houde Han
, Jicheng Jin^*
, Xiaonan Wu

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

43 Citations (Scopus)

Abstract

A finite-difference scheme is proposed for the one-dimensional time-dependent Schrödinger 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.

Original language	English
Pages (from-to)	1345-1362
Number of pages	18
Journal	Computers and Mathematics with Applications
Volume	50
Issue number	8-9
DOIs	https://doi.org/10.1016/j.camwa.2005.05.006
Publication status	Published - Oct 2005

User-Defined Keywords

Artificial boundary conditions
Finite-difference method
The Schrödinger equation

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10.1016/j.camwa.2005.05.006

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title = "A finite-difference method for the one-dimensional time-dependent schr{\"o}dinger equation on unbounded domain",

abstract = "A finite-difference scheme is proposed for the one-dimensional time-dependent Schr{\"o}dinger 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.",

keywords = "Artificial boundary conditions, Finite-difference method, The Schr{\"o}dinger equation",

author = "Houde Han and Jicheng Jin and Xiaonan Wu",

note = "Funding Information: *The research is partly supported by the Special Funds for Major State Basic Research Projects of China. t Author to whom all correspondence should be addressed. SThe research is supported by RCC of Hong Kong and FRG of Hong Kong Baptist University. The authors wish to thank the referees for many valuable suggestions.",

year = "2005",

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doi = "10.1016/j.camwa.2005.05.006",

language = "English",

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T1 - A finite-difference method for the one-dimensional time-dependent schrödinger equation on unbounded domain

AU - Han, Houde

AU - Jin, Jicheng

AU - Wu, Xiaonan

N1 - Funding Information: *The research is partly supported by the Special Funds for Major State Basic Research Projects of China. t Author to whom all correspondence should be addressed. SThe research is supported by RCC of Hong Kong and FRG of Hong Kong Baptist University. The authors wish to thank the referees for many valuable suggestions.

PY - 2005/10

Y1 - 2005/10

N2 - A finite-difference scheme is proposed for the one-dimensional time-dependent Schrödinger 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.

AB - A finite-difference scheme is proposed for the one-dimensional time-dependent Schrödinger 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.

KW - Artificial boundary conditions

KW - Finite-difference method

KW - The Schrödinger equation

UR - https://www.scopus.com/pages/publications/28844493429

U2 - 10.1016/j.camwa.2005.05.006

DO - 10.1016/j.camwa.2005.05.006

M3 - Journal article

AN - SCOPUS:28844493429

SN - 0898-1221

VL - 50

SP - 1345

EP - 1362

JO - Computers and Mathematics with Applications

JF - Computers and Mathematics with Applications

IS - 8-9

ER -

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

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