WIAS Preprint No. 66, (1993)

On Stationary Schrödinger-Poisson Equations


  • Kaiser, Hans-Christoph
  • Rehberg, Joachim
  • Albinus, Günther

2010 Mathematics Subject Classification

  • 35J05 35P15 47H05


  • Stationäry Schrödinger-Poisson system, monotone potential operators, iterative methods, discretization of the Schrödinger-Poisson system, electron gas with reduced dimension, nanoelectronics




We regard the Schrödinger-Poisson system arising from the modelling of an electron gas with reduced dimension in a bounded up to three-dimensional domain and establish the method of steepest descent. The electrostatic potentials of the iteration scheme will converge uniformly on the spatial domain. To get this result we investigate the Schrödinger operator, the Fermi level and the quantum mechanical electron density operator for square integrable electrostatic potentials. On bounded sets of potentials the Fermi level is continuous and boundeq, and the electron density operator is monotone and Lipschitz continuous. - As a tool we develop a Riesz-Dunford functional calculus for semibounded self-adjoint operators using paths of integration which enclose a real half axis.

Appeared in

  • Math. Methods Appl. Sci., 20 (1997), pp. 1283-1312

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