On absolute continuity of the spectrum of a periodic magnetic Schrödinger operator

Abstract

We consider the Schrödinger operator in ${\mathbb{R}}^n$, $n\ge 3$, with the electric potential $V$ and the magnetic potential $A$ being periodic functions (with a common period lattice) and prove absolute continuity of the spectrum of the operator in question under some conditions which, in particular, are satisfied if $V\in L_{\mathrm{loc}}^{n/2}({\mathbb{R}}^n)$ and $A\in H_{\mathrm{loc}}^q({\mathbb{R}}^n;{\mathbb{R}}^n)$, $q>(n-1)/2$.

25 pages

References in corpus (1)

• On absolute continuity of the spectrum of a d-dimensional periodic magnetic Dirac operator