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Volume 4, Issue 4
A Review of Transparent and Artificial Boundary Conditions Techniques for Linear and Nonlinear Schrödinger Equations

Xavier Antoine, Anton Arnold, Christophe Besse, Matthias Ehrhardt & Achim Schädle

Commun. Comput. Phys., 4 (2008), pp. 729-796.

Published online: 2008-04

[An open-access article; the PDF is free to any online user.]

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  • Abstract

In this review article we discuss different techniques to solve numerically the time-dependent Schrödinger equation on unbounded domains. We present in detail the most recent approaches and describe briefly alternative ideas pointing out the relations between these works. We conclude with several numerical examples from different application areas to compare the presented techniques. We mainly focus on the one-dimensional problem but also touch upon the situation in two space dimensions and the cubic nonlinear case.

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COPYRIGHT: © Global Science Press

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@Article{CiCP-4-729, author = {Xavier Antoine, Anton Arnold, Christophe Besse, Matthias Ehrhardt and Achim Schädle}, title = {A Review of Transparent and Artificial Boundary Conditions Techniques for Linear and Nonlinear Schrödinger Equations}, journal = {Communications in Computational Physics}, year = {2008}, volume = {4}, number = {4}, pages = {729--796}, abstract = {

In this review article we discuss different techniques to solve numerically the time-dependent Schrödinger equation on unbounded domains. We present in detail the most recent approaches and describe briefly alternative ideas pointing out the relations between these works. We conclude with several numerical examples from different application areas to compare the presented techniques. We mainly focus on the one-dimensional problem but also touch upon the situation in two space dimensions and the cubic nonlinear case.

}, issn = {1991-7120}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cicp/7814.html} }
TY - JOUR T1 - A Review of Transparent and Artificial Boundary Conditions Techniques for Linear and Nonlinear Schrödinger Equations AU - Xavier Antoine, Anton Arnold, Christophe Besse, Matthias Ehrhardt & Achim Schädle JO - Communications in Computational Physics VL - 4 SP - 729 EP - 796 PY - 2008 DA - 2008/04 SN - 4 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/cicp/7814.html KW - AB -

In this review article we discuss different techniques to solve numerically the time-dependent Schrödinger equation on unbounded domains. We present in detail the most recent approaches and describe briefly alternative ideas pointing out the relations between these works. We conclude with several numerical examples from different application areas to compare the presented techniques. We mainly focus on the one-dimensional problem but also touch upon the situation in two space dimensions and the cubic nonlinear case.

Xavier Antoine, Anton Arnold, Christophe Besse, Matthias Ehrhardt and Achim Schädle. (2008). A Review of Transparent and Artificial Boundary Conditions Techniques for Linear and Nonlinear Schrödinger Equations. Communications in Computational Physics. 4 (4). 729-796. doi:
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