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A QUANTUM TRANSMITTING SCHRÖDINGER–POISSON SYSTEM

M. BARO

Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstr. 39, 10117 Berlin, Germany

Supported by the DFG Research Center "Mathematics for key technologies" (FZT 86) in Berlin.

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H.-CHR. KAISER

Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstr. 39, 10117 Berlin, Germany

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H. NEIDHARDT

Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstr. 39, 10117 Berlin, Germany

Supported by the DFG under grant RE 1480/2.

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, and

J. REHBERG

Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstr. 39, 10117 Berlin, Germany

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https://doi.org/10.1142/S0129055X04001996Cited by:13 (Source: Crossref)

Abstract

We study a stationary Schrödinger–Poisson system on a bounded interval of the real axis. The Schrödinger operator is defined on the bounded domain with transparent boundary conditions. This allows us to model a non-zero current through the boundary of the interval. We prove that the system always admits a solution and give explicit a priori estimates for the solutions.

To our fathers

Keywords:

AMSC: 34B24, 34L40, 47B44, 81U20, 82D37

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