Asymptotic analysis of a Schrödinger-Poisson system with quantum wells and macroscopic nonlinearities in dimension 1

Abstract

We consider the stationary one dimensional Schrödinger-Poisson system on a bounded interval with a background potential describing a quantum well. Using a partition function which forces the particles to remain in the quantum well, the limit $h\to 0$ in the nonlinear system leads to a uniquely solved nonlinear problem with concentrated particle density. It allows to conclude about the convergence of the solution.

18 pages