On absolute continuity of the spectrum of periodic Schrödinger operators

Abstract

In this paper we find a new condition on a real periodic potential for which the self-adjoint Schrödinger operator may be defined by a quadratic form and the spectrum of the operator is purely absolutely continuous. This is based on resolvent estimates and spectral projection estimates in weighted $L^2$ spaces on the torus, and an oscillatory integral theorem.

To appear in Monatsh. Math., 17 pages

References in corpus (2)

• From resolvent estimates to unique continuation for the Schrödinger equation
• A note on local behavior of eigenfunctions of the Schrödinger operator