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The Gaussian Beam Methods for Schrödinger-Poisson Equations

The Gaussian Beam Methods for Schrödinger-Poisson Equations
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Year:    2010

Journal of Computational Mathematics, Vol. 28 (2010), Iss. 2 : pp. 261–272

Abstract

As an important model in quantum semiconductor devices, the Schrödinger-Poisson equations have generated widespread interests in both analysis and numerical simulations in recent years. In this paper, we present Gaussian beam methods for the numerical simulation of the one-dimensional Schrödinger-Poisson equations. The Gaussian beam methods for high frequency waves outperform the geometrical optics method in that the former are accurate even around caustics. The purposes of the paper are first to develop the Gaussian beam methods, based on our previous methods for the linear Schrödinger equation, for the Schrödinger-Poisson equations, and then check their validity for this weakly-nonlinear system.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jcm.2009.10-m1005

Journal of Computational Mathematics, Vol. 28 (2010), Iss. 2 : pp. 261–272

Published online:    2010-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    12

Keywords:    Schrödinger-Poisson equations Gaussian beam methods Vlasov-Poisson equations.

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