Michael Baro, Hans-Christoph Kaiser, Hagen Neidhardt, and Joachim Rehberg
A quantum transmitting Schroedinger-Poisson system
(696K, pdf)

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