TY - GEN A1 - Antoine, Xavier A1 - Arnold, Anton A1 - Besse, Christophe A1 - Ehrhardt, Matthias A1 - Schädle, Achim T1 - A Review of Transparent and Artificial Boundary Conditions Techniques for Linear and Nonlinear Schrödinger Equations N2 - 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. KW - Schrödinger equation KW - transparent boundary condition KW - discrete convolution KW - unbounded domain Y1 - 2009 UR - https://opus4.kobv.de/opus4-matheon/frontdoor/index/index/docId/433 UR - https://nbn-resolving.org/urn:nbn:de:0296-matheon-4339 ER -