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Main Title: Fast Calculation of Energy and Mass preserving solutions of Schrödinger-Poisson systems on unbounded domains
Author(s): Ehrhardt, Matthias
Zisowsky, Andrea
Type: Research Paper
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.
Subject(s): Schrödinger-Poisson system
Schrödinger equation
finite differences
discrete transparent boundary conditions
difference equation
Newton potential
Issue Date: 8-Oct-2004
Date Available: 11-May-2022
Language Code: en
DDC Class: 510 Mathematik
Series: Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin
Series Number: 2004, 32
ISSN: 2197-8085
TU Affiliation(s): Fak. 2 Mathematik und Naturwissenschaften » Inst. Mathematik
Appears in Collections:Technische Universität Berlin » Publications

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