Stability of a Szegő-type asymptotics

Abstract

We consider a multi-dimensional continuum Schrödinger operator H which is given by a perturbation of the negative Laplacian by a compactly supported bounded potential. We show that, for a fairly large class of test functions, the second-order Szegőtype asymptotics for the spatially truncated Fermi projection of H is independent of the potential and, thus, identical to the known asymptotics of the Laplacian.