Absolutely continuous spectrum of a typical Schrödinger operator with a slowly decaying potential

Abstract

We consider a family of multi-dimensional Schrödinger operators $-\Delta +tV$ with a real $t$. The potential $V$ in our model decays at infinity in a special way, so that it satisfies a certain integral condition. We prove that the absolutely continuous spectrum of this operator covers the interval $[0,\infty )$ for almost every $t$.

arXiv admin note: substantial text overlap with arXiv:1106.1712

References in corpus (1)

• Absolutely continuous spectrum of a one-paramentric family of Schrödinger operators

Cited by in corpus (1)

• Multidimensional L2 conjecture: a survey