Absorbing boundary conditions for the one-dimensional Schrödinger equation with an exterior repulsive potential |
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| Authors: | Xavier Antoine Christophe Besse Pauline Klein |
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| Institution: | 1. Institut Elie Cartan Nancy, Nancy-Université, CNRS UMR 7502, INRIA CORIDA Team, Boulevard des Aiguillettes B.P. 239, F-54506 Vandoeuvre-lès-Nancy, France;2. Equipe Projet Simpaf – Inria CR Lille Nord Europe, Laboratoire Paul Painlevé, Unité Mixte de Recherche CNRS (UMR 8524), UFR de Mathématiques Pures et Appliquées, Université des Sciences et Technologies de Lille, Cité Scientifique, 59655 Villeneuve d’Ascq Cedex, France |
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| Abstract: | Mathematical constructions and comparisons of accurate absorbing boundary conditions for the one-dimensional Schrödinger equation with a general variable repulsive potential are developed. Stable semi-discretization schemes are built for the associated initial boundary value problems. Finally, some numerical simulations give a comparison of the various absorbing boundary conditions and show that they yield accurate computations. |
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