On a one-dimensional Schrödinger-Poisson scattering model

Naoufel Ben Abdallah*, Pierre Degond, Peter A. Markowich

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

78 Scopus citations


A Schrödinger - Poisson model describing the stationary behavior of a quantum device away from equilibrium is proposed and analyzed. In this model, current carrying scattering states of the Schrödinger equation are considered. The potential is coupled to the Schrödinger equation through the density matrix defined according to a prescribed statistics. Existence of solutions is proven. The semiclassical limit is performed via a Wigner transform which leads to the standard boundary value problem for the semiclassical Vlasov-Poisson system. Finally, a high injection asymptotics is investigated.

Original languageEnglish (US)
Pages (from-to)135-155
Number of pages21
JournalZeitschrift fur Angewandte Mathematik und Physik
Issue number1
StatePublished - Jan 1997
Externally publishedYes


  • Current carrying state
  • Inflow boundary condition
  • Quantum phenomena
  • Semiclassical unit
  • Vlasov equation
  • Wigner transform

ASJC Scopus subject areas

  • Mathematics(all)
  • Physics and Astronomy(all)
  • Applied Mathematics


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