On Stationary Schrödinger-Poisson Equations

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

Analyticity for some operator functions from statistical quantum mechanics : dedicated to Günter Albinus

For rather general thermodynamic equilibrium distribution functions the density of a statistical ensemble of quantum mechanical particles depends analytically on the potential in the Schrödinger operator describing the quantum system. A key to the proof is that the resolvent to a power less than one of an elliptic operator with non-smooth coefficients, and mixed Dirichlet/Neumann boundary conditions on a bounded up to three-dimensional Lipschitz domain factorizes over the space of essentially bounded functions