On a multidimensional Schrödinger–Poisson scattering model for semiconductors

We consider a stationary Schrödinger–Poisson problem modeling a self-consistent transport in a quantum coupler. The Schrödinger equation is set on a bounded domain with transparent boundary conditions describing incoming scattering states of the Schrödinger operator. The coupling with the Poisson eq...

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Bibliographic Details
Published in:Journal of mathematical physics 2000-07, Vol.41 (7), p.4241-4261
Main Author: Abdallah, Naoufel Ben
Format: Article
Language:English
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Summary:We consider a stationary Schrödinger–Poisson problem modeling a self-consistent transport in a quantum coupler. The Schrödinger equation is set on a bounded domain with transparent boundary conditions describing incoming scattering states of the Schrödinger operator. The coupling with the Poisson equation is done thanks to a nonlinear limiting absorption procedure. The charge density of the limit potential is shown to be equal to the sum of the scattering state and bound state densities.
ISSN:0022-2488
1089-7658
DOI:10.1063/1.533397