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

Shi Jin, Hao Wu & Xu Yang

DOI: 10.4208/jcm.2009.10-m1005

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 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.

  • Keywords

Schrödinger-Poisson equations, Gaussian beam methods, Vlasov-Poisson equations.

  • 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 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.

}, 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://doi.org/10.4208/jcm.2009.10-m1005 UR - https://global-sci.org/intro/article_detail/jcm/8518.html KW - Schrödinger-Poisson equations, Gaussian beam methods, Vlasov-Poisson equations. AB -

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.

Shi Jin, Hao Wu and Xu Yang. (2010). 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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