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Absorbing Boundary Conditions for Solving N-Dimensional Stationary Schrödinger Equations with Unbounded Potentials and Nonlinearities

Published online by Cambridge University Press:  20 August 2015

Pauline Klein ,
Xavier Antoine ,
Christophe Besse  and
Matthias Ehrhardt
Pauline Klein*
Affiliation:
Institut Elie Cartan Nancy, Nancy-Université, CNRS UMR 7502, INRIA CORIDA Team, Boulevard des Aiguillettes B.P. 239, 54506 Vandœuvre-lès-Nancy, France
Xavier Antoine*
Affiliation:
Institut Elie Cartan Nancy, Nancy-Université, CNRS UMR 7502, INRIA CORIDA Team, Boulevard des Aiguillettes B.P. 239, 54506 Vandœuvre-lès-Nancy, France
Christophe Besse*
Affiliation:
Laboratoire Paul Painlevé, CNRS UMR 8524, Simpaf Project Team-Inria CR Lille Nord Europe, Université des Sciences et Technologies de Lille, Cité Scientifique, 59655 Villeneuve d’Ascq Cedex, France
Matthias Ehrhardt*
Affiliation:
Lehrstuhl für Angewandte Mathematik und Numerische Analysis, Fachbereich C-Mathematik und Naturwissenschaften, Bergische Universität Wuppertal, Gaufistr. 20, 42119 Wuppertal, Germany
*
Email:pauline.klein@iecn.u-nancy.fr
Corresponding author.Email:xavier.antoine@iecn.u-nancy.fr
Email:christophe.besse@math.univ-lille1.fr
Email:ehrhardt@math.uni-wuppertal.de
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Abstract

We propose a hierarchy of novel absorbing boundary conditions for the one-dimensional stationary Schrödinger equation with general (linear and nonlinear) potential. The accuracy of the new absorbing boundary conditions is investigated numerically for the computation of energies and ground-states for linear and nonlinear Schrödinger equations. It turns out that these absorbing boundary conditions and their variants lead to a higher accuracy than the usual Dirichlet boundary condition. Finally, we give the extension of these ABCs to N-dimensional stationary Schrödinger equations.

Keywords

35J1065M6065N30Absorbing boundary conditionsstationary Schrödinger equationsunbounded domainspatially dependent potentialground states computation
Type
Research Article
Information
Communications in Computational Physics , Volume 10 , Issue 5 , November 2011 , pp. 1280 - 1304
Copyright
Copyright © Global Science Press Limited 2011

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