Keywords:
Forschungsbericht
Description / Table of Contents:
We propose transparent boundary conditions (TBCs) for the time-dependent Schrödinger equation on a circular computational domain. First we derive the two-dimensional discrete TBCs in conjunction with a conservative Crank-Nicolson finite difference scheme. The presented discrete initial boundary-value problem is unconditionally stable and completely reflection-free at the boundary. Then, since the discrete TBCs for the Schrödinger equation with a spatially dependent potential include a convolution w.r.t. time with a weakly decaying kernel, we construct approximate discrete TBCs with a kernel having the form of a finite sum of exponentials, which can be efficiently evaluated by recursion. In numerical tests we finally illustrate the accuracy, stability, and efficiency of the proposed method. As a by-product we also present a new formulation of discrete TBCs for the 1D Schrödinger equation, with convolution coefficients that have better decay properties than those from the literature.
Type of Medium:
Online Resource
Pages:
Online-Ressource (41 S., 1,97 MB)
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graph. Darst.
Series Statement:
Preprint / Weierstraß-Institut für Angewandte Analysis und Stochastik 1344
URL:
http://webdoc.sub.gwdg.de/ebook/serien/e/wias/2008/wias_preprints_1344.pdf
URL:
https://edocs.tib.eu/files/e01fn11/573542732.pdf
Language:
English
Note:
Unterschiede zwischen dem gedruckten Dokument und der elektronischen Ressource können nicht ausgeschlossen werden. - Auch als gedr. Ausg. vorhanden
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Systemvoraussetzungen: Acrobat reader.
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