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)
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.