A Review of Transparent and Artificial Boundary Conditions Techniques for Linear and Nonlinear Schr�dinger Equations

By Xavier Antoine, Anton Arnold, Christophe Besse, Matthias Ehrhardt, A. Schädle. Communications in Computational Physics, 2008

344 citations recorded by the source corpus.

In this review article we discuss different techniques to solve numerically the time-dependent Schrodinger equation on unbounded domains. We present in de- tail 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 dimen- sions and the cubic nonlinear case.

Subfields: Electrical and Electronic Engineering, Numerical Analysis, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/426fb4ac30d31ac7f05fe2b90ffbf3a7d56928eb