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

Research output: Contribution to journalArticlepeer-review

35 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 languageEnglish
Pages (from-to)1345-1362
Number of pages18
JournalComputers and Mathematics with Applications
Volume50
Issue number8-9
DOIs
Publication statusPublished - Oct 2005

Scopus Subject Areas

  • Modelling and Simulation
  • Computational Theory and Mathematics
  • Computational Mathematics

User-Defined Keywords

  • Artificial boundary conditions
  • Finite-difference method
  • The Schrödinger equation

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