Volume 28, Issue 2
The Gaussian Beam Methods for Schrödinger-Poisson Equations

Shi Jin, Hao Wu & Xu Yang

J. Comp. Math., 28 (2010), pp. 261-272.

Published online: 2010-04

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  • Abstract

As an important model in quantum semiconductor devices, the Schr\"odinger-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 Schrodinger-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 Schr\"odinger equation, for the Schr\"odinger-Poisson equations, and then check their validity for this weakly-nonlinear system.

  • Keywords

Schrödinger-Poisson equations Gaussian beam methods

  • AMS Subject Headings

81Q20 65M99

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-28-261, author = {Shi Jin, Hao Wu and Xu Yang}, title = {The Gaussian Beam Methods for Schrödinger-Poisson Equations}, journal = {Journal of Computational Mathematics}, year = {2010}, volume = {28}, number = {2}, pages = {261--272}, abstract = {

As an important model in quantum semiconductor devices, the Schr\"odinger-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 Schrodinger-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 Schr\"odinger equation, for the Schr\"odinger-Poisson equations, and then check their validity for this weakly-nonlinear system.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.2009.10-m1005}, url = {http://global-sci.org/intro/article_detail/jcm/8518.html} }
TY - JOUR T1 - The Gaussian Beam Methods for Schrödinger-Poisson Equations AU - Shi Jin, Hao Wu & Xu Yang JO - Journal of Computational Mathematics VL - 2 SP - 261 EP - 272 PY - 2010 DA - 2010/04 SN - 28 DO - http://dor.org/10.4208/jcm.2009.10-m1005 UR - https://global-sci.org/intro/article_detail/jcm/8518.html KW - Schrödinger-Poisson equations KW - Gaussian beam methods KW - AB -

As an important model in quantum semiconductor devices, the Schr\"odinger-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 Schrodinger-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 Schr\"odinger equation, for the Schr\"odinger-Poisson equations, and then check their validity for this weakly-nonlinear system.

Shi Jin, Hao Wu & Xu Yang. (1970). The Gaussian Beam Methods for Schrödinger-Poisson Equations. Journal of Computational Mathematics. 28 (2). 261-272. doi:10.4208/jcm.2009.10-m1005
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