Preprint 37-2007

A Review of Artificial Boundary Conditions for the Schrödinger Equation

Author(s) : Xavier Antoine , Anton Arnold , Christophe Besse , Matthias Ehrhardt , Achim Schädle

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 37-2007

PACS : 02.70.Bf, 31.15.Fx

Abstract :
In this review we discuss techniques to solve numerically the time-dependent linear Schrödinger equation on unbounded domains. We present some recent approaches and describe alternative ideas pointing out the relations between these works.

Keywords : Schrödinger equation, transparent boundary conditions, discrete convolution, unbounded domain, finite difference schemes, finite elements

Notes :
Proceedings of ICIAM07, the 6th International Congress on Industrial and Applied Mathematics, Zürich, Switzerland, 16-20 July 2007, Minisymposium Artificial Boundary Conditions for linear and nonlinear Schrödinger equations.