Geodesic
Asymptotic Analysis of a Schrödinger-Poisson System with Quantum Wells and Macroscopic Nonlinearities in Dimension 1
Serdica Mathematical Journal, Tome 35 (2010) no. 1, pp. 11-38.

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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®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.
Keywords: Schrödinger-Poisson System, Asymptotic Analysis, Semi-Classical Analysis, Spectral Theory 
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     author = {Faraj, A.},
     title = {Asymptotic {Analysis} of a {Schr\"odinger-Poisson} {System} with {Quantum} {Wells} and {Macroscopic} {Nonlinearities} in {Dimension} 1},
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Faraj, A. Asymptotic Analysis of a Schrödinger-Poisson System with Quantum Wells and Macroscopic Nonlinearities in Dimension 1. Serdica Mathematical Journal, Tome 35 (2010) no. 1, pp. 11-38. http://geodesic.mathdoc.fr/item/SMJ2_2010_35_1_a1/