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

Ali Faraj (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

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 $h\rightarrow0$ 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.

Mots clés: Spectral theory; Schrödinger-Poisson system; Asymptotic analysis; Semi-classical analysis; Spectral theory.

Domaines: Equations aux dérivées partielles [math.AP]

Ali Faraj. Asymptotic analysis of a Schrödinger-Poisson system with quantum wells and macroscopic nonlinearities in dimension 1. 2009. ⟨hal-00450037v1⟩