TY - GEN A1 - Arnold, Anton A1 - Ehrhardt, Matthias A1 - Schulte, Maike A1 - Sofronov, Ivan T1 - Discrete transparent boundary conditions for the two dimensional Schrödinger equation N2 - This paper is concerned with transparent boundary conditions (TBCs) for the time-dependent Schrödinger equation on a circular domain. Discrete TBCs are introduced in the numerical simulations of problems on unbounded domains in order to reduce the computational domain to a finite region in order to make this problem feasible for numerical simulations. The main focus of this article is on the appropriate discretization of such TBCs for the two-dimensional Schrödinger equation in conjunction with a conservative Crank-Nicolson-type finite difference discretization. The presented discrete TBCs yield an unconditionally stable numerical scheme and are completely reflection-free at the boundary. Furthermore we prove concisely the stability of the recurrence formulas used to obtain the convolution coefficients of the new discrete TBC for a spatially dependent potential. KW - two-dimensional Schrödinger equation KW - transparent boundary KW - conditions KW - discrete convolution KW - finite difference schemes Y1 - 2006 UR - https://opus4.kobv.de/opus4-matheon/frontdoor/index/index/docId/341 UR - https://nbn-resolving.org/urn:nbn:de:0296-matheon-3411 ER -