Asymptotic analysis of a Schr\"odinger-Poisson system with quantum wells and macroscopic nonlinearities in dimension 1
Abstract
We consider the stationary one dimensional Schr\"odinger-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→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.
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