Absorbing Boundary Conditions for Solving N-Dimensional Stationary Schrödinger Equations with Unbounded Potentials and Nonlinearities
Pauline KleinInstitut Elie Cartan Nancy, Nancy-Université, CNRS UMR 7502, INRIA CORIDA Team, Boulevard des Aiguillettes B.P. 239, 54506 Vandœuvre-lès-Nancy, FranceXavier AntoineInstitut Elie Cartan Nancy, Nancy-Université, CNRS UMR 7502, INRIA CORIDA Team, Boulevard des Aiguillettes B.P. 239, 54506 Vandœuvre-lès-Nancy, FranceChristophe BesseLaboratoire 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, FranceMatthias EhrhardtLehrstuhl für Angewandte Mathematik und Numerische Analysis, Fachbereich C-Mathematik und Naturwissenschaften, Bergische Universität Wuppertal, Gaufistr. 20, 42119 Wuppertal, Germany
2011en
ABI
Аннотация
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.
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