@article{AntoineArnoldBesseetal.2008, author = {Antoine, Xavier and Arnold, Anton and Besse, Christophe and Ehrhardt, Matthias and Sch{\"a}dle, Achim}, title = {A Review of Transparent and Artificial Boundary Conditions Techniques for Linear and Nonlinear Schr{\"o}dinger Equations}, volume = {4}, journal = {Commun. Comput. Phys.}, pages = {729 -- 796}, year = {2008}, language = {en} } @misc{AntoineArnoldBesseetal.2007, author = {Antoine, Xavier and Arnold, Anton and Besse, Christophe and Ehrhardt, Matthias and Sch{\"a}dle, Achim}, title = {A Review of Transparent and Artificial Boundary Conditions Techniques for Linear and Nonlinear Schr{\"o}dinger Equations}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-10332}, number = {07-34}, year = {2007}, abstract = {In this review article we discuss different techniques to solve numerically the time-dependent Schr{\"o}dinger 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.}, language = {en} }