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Preprint 32-2004

Fast Calculation of Energy and Mass preserving solutions of Schrödinger-Poisson systems on unbounded domains

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Author(s) : Matthias Ehrhardt , Andrea Zisowsky

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 32-2004

PACS : 02.70.Bf, 31.15.Fx, 95.30.Cq

Abstract :
This paper deals with the numerical solution of the time-dependent Schrödinger-Poisson system in the spherically symmetric case. Since the problem is posed on an unbounded domain one has to introduce artificial boundary conditions to confine the computational domain. The main topic of this work is the construction of a so-called discrete transparent boundary condition (TBC) for a Crank-Nicolson-type predictor-corrector scheme for solving the Schrödinger-Poisson system. This scheme has the property of mass and energy conservation exactly on the discrete level. We propose different strategies for the discrete TBC and present an efficient implementation. Finally, a numerical example illustrate the findings and shows the comparison results between the different approaches.

Keywords : Schrödinger-Poisson system, Schrödinger equation, finite differences, discrete transparent boundary conditions, difference equation, Newton potential

Notes :
submitted to: Journal of Computational and Applied Mathematics

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