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

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

2011-11-23

arxiv.org/abs/1111.5552v2

Physics

Mathematical Physics

arXiv admin note: substantial text overlap with arXiv:1106.1712

Scientific paper

We consider a family of multi-dimensional Schr\"odinger operators $-\Delta+t
V$ 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 $t$.

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