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Article Dans Une Revue Serdica Mathematical Journal Année : 2010

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

Ali Faraj
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Résumé

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.
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Dates et versions

hal-00450037 , version 1 (25-01-2010)
hal-00450037 , version 2 (16-03-2010)

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Ali Faraj. Asymptotic analysis of a Schrödinger-Poisson system with quantum wells and macroscopic nonlinearities in dimension 1. Serdica Mathematical Journal, 2010, 36 (1), pp.11-38. ⟨hal-00450037v2⟩
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