WIAS Preprint No. 814, (2003)

A quantum transmitting Schrödinger-Poisson system


  • Baro, Michael
  • Kaiser, Hans-Christoph
  • Neidhardt, Hagen
  • Rehberg, Joachim

2010 Mathematics Subject Classification

  • 34B24 34L40 47B44 81U20 82D37

2008 Physics and Astronomy Classification Scheme

  • 85.35.-p


  • Quantum phenomena, current carrying state, inflow boundary condition, dissipative operators, open quantum systems, carrier and current densities, density matrices, quantum transmitting boundary method


We consider a stationary Schroedinger-Poisson system on a bounded interval of the real axis. The Schroedinger operator is defined on the bounded domain with transparent boundary conditions. This allows to model a non-zero current flow trough the boundary of the interval. We prove that the system always admits a solution and give explicit a priori estimates for the solutions.

Appeared in

  • Reviews in Mathematical Physics, 2004, Vol. 16, No. 3, pp. 281-330

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