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Stationary Solutions of Quasi-Linear Schrödinger–Poisson Systems

✍ Scribed by R. Illner; O. Kavian; H. Lange

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
257 KB
Volume
145
Category
Article
ISSN
0022-0396

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✦ Synopsis

We show that a high-field version of the periodic Schro dinger Poisson system including nonlinear terms in the Poisson equation (corresponding to a fielddependent dielectric constant) and effective potentials in the Schro dinger equation has an infinite number of different stationary states which correspond to solutions of a nonlinear Schro dinger Poisson eigenvalue problem.

1998 Academic Press

1. Introduction

We are concerned with the study of a quantum mechanical model of extremely small devices in semi-conductor nanostructures (such as quantum-wires) where the quantum structure has to be taken into account. In theoretical and numerical studies, the most frequently considered model is the self-consistent Schro dinger Poisson system (SP). In the physics literature, numerical computations have been performed and published by many authors (see Refs. 1 5); mostly, mixed boundary conditions on a finite two-or three-dimensional domain (e.g., rectangles) have been considered in numerical calculations.

Mathematical studies on (SP) have been carried out by Brezzi and Markowich (6) , Illner, Lange, and Zweifel (7) (whole space 3D Cauchy article no. DE973405

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