Singularities of the magnetic spectral shift function for potentials of variable sign

Abstract

We consider the 3D-Schrödinger operator $H_0$ with constant magnetic field $B$ of scalar intensity $b>0$, and its perturbations $H=H_0+V$ by a potential $V$ of not necessarily fixed sign. Then we study the singularities at the Landau levels of the Kreĭn spectral shift functions $\xi (\cdot ;H,H_0)$ for the pair $(H,H_0)$. We consider power-like decaying potentials and cylindrically supported potentials (with axis $B$).