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We consider a stationary Schrödinger-Poisson system on a bounded interval of the real axis. The Schrödinger 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… (More)
Dedicated to Konrad Gröger — teacher, colleague, friend — on the occasion of his 65 th birthday. Key words and phrases. non–selfadjoint Schrödinger–type operators, spectral asymp-totics, Abel basis of root vectors, dissipative operators, open quantum systems.
Classical solutions of drift–diffusion equations 1 Abstract We regard drift–diffusion equations for semiconductor devices in Lebesgue spaces. To that end we reformulate the (generalized) van Roosbroeck system as an evolution equation for the potentials to the driving forces of the currents of electrons and holes. This evolution equation falls into a class… (More)
We present a node-centered finite volume method for computing a representative range of eigenvalues and eigenvectors of the Schrödinger operator on a three-dimensional cylindrically symmetric bounded domain with mixed boundary conditions. More specifically, we deal with a semiconductor nanowire which consists of a dominant host material and contains… (More)