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Volume 10, Issue 5
Absorbing Boundary Conditions for Solving N-Dimensional Stationary Schrödinger Equations with Unbounded Potentials and Nonlinearities

Pauline Klein, Xavier Antoine, Christophe Besse & Matthias Ehrhardt

DOI: 10.4208/cicp.251010.160211a

Commun. Comput. Phys., 10 (2011), pp. 1280-1304.

Published online: 2011-10

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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.

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@Article{CiCP-10-1280, author = {Pauline Klein, Xavier Antoine, Christophe Besse and Matthias Ehrhardt}, title = {Absorbing Boundary Conditions for Solving N-Dimensional Stationary Schrödinger Equations with Unbounded Potentials and Nonlinearities}, journal = {Communications in Computational Physics}, year = {2011}, volume = {10}, number = {5}, pages = {1280--1304}, 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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.251010.160211a}, url = {http://global-sci.org/intro/article_detail/cicp/7484.html} }
TY - JOUR T1 - Absorbing Boundary Conditions for Solving N-Dimensional Stationary Schrödinger Equations with Unbounded Potentials and Nonlinearities AU - Pauline Klein, Xavier Antoine, Christophe Besse & Matthias Ehrhardt JO - Communications in Computational Physics VL - 5 SP - 1280 EP - 1304 PY - 2011 DA - 2011/10 SN - 10 DO - http://doi.org/10.4208/cicp.251010.160211a UR - https://global-sci.org/intro/article_detail/cicp/7484.html KW - AB -

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.

Pauline Klein, Xavier Antoine, Christophe Besse and Matthias Ehrhardt. (2011). Absorbing Boundary Conditions for Solving N-Dimensional Stationary Schrödinger Equations with Unbounded Potentials and Nonlinearities. Communications in Computational Physics. 10 (5). 1280-1304. doi:10.4208/cicp.251010.160211a
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