A. Arnold, M. Ehrhardt, M. Schulte, I. Sofronov:

"Discrete transparent boundary conditions for the Schrödinger equation on circular domains";

in: "ASC Report 31/2008", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2008, ISBN: 978-3-902627-01-8.

We propose transparent boundary conditions (TBCs) for the time-

dependent Schršodinger equation on a circular computational domain.

First we derive the two-dimensional discrete TBCs in conjunction with

a conservative Crank-Nicolson finite difference scheme. The presented

discrete initial boundary-value problem is unconditionally stable and

completely reflection-free at the boundary. Then, since the discrete

TBCs for the Schršodinger equation with a spatially dependent potential

include a convolution w.r.t. time with a weakly decaying kernel, we

construct approximate discrete TBCs with a kernel having the form of

a finite sum of exponentials, which can be efficiently evaluated by recursion.

In numerical tests we finally illustrate the accuracy, stability,

and efficiency of the proposed method.

two-dimensional Schršodinger equation, transparent boundary

http://www.asc.tuwien.ac.at/preprint/2008/asc31x2008.pdf

Created from the Publication Database of the Vienna University of Technology.