Analysis of high-order absorbing boundary conditions for the Schrödinger equation

Jiwei Zhang, Zhizhong Sun, Xiaonan WU*, Desheng Wang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

15 Citations (Scopus)

Abstract

The paper is concerned with the numerical solution of Schr ̈odinger equations on an unbounded spatial domain. High-order absorbing boundary conditions for one-dimensional domain are derived, and the stability of the reduced initial boundary value problem in the computational interval is proved by energy estimate. Then a second order finite difference scheme is proposed, and the convergence of the scheme is established as well. Finally, numerical examples are reported to confirm our error estimates of the numerical methods.

Original languageEnglish
Pages (from-to)742-766
Number of pages25
JournalCommunications in Computational Physics
Volume10
Issue number3
DOIs
Publication statusPublished - Sep 2011

Scopus Subject Areas

  • Physics and Astronomy (miscellaneous)

User-Defined Keywords

  • Convergence
  • Finite differencemethod
  • High-order absorbing boundary condition
  • Schrodinger equation

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