On the Green Function of the Landau Operator and its Properties Related to Point Interactions

Abstract

The Green function $G$ of the Schrödinger operator with a magnetic field (i.e. the Landau operator) $H$ is studied. Two representations of $G$ are used, namely in form of an integral and of a series. The space-variable asymptotics as well as the energetic ones are obtained. The analytical and asymptotical properties of $G$ we obtain are related to point perturbations of $H$.