Global trace asymptotics in the self-generated magnetic field in the case of Coulomb-like singularities

Abstract

We consider a semiclassical asymptotics of local trace for the 3D-Schroedinger operator with self-generated magnetic field in the case when electric potential has one or several Coulomb-like singularities; it is given by Weyl expression plus (magnetic) Scott correction term with O(h^{-4/3}) error provided distance between singularities is large enough. Significant improvement and simplification in comparison to v1.