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

2011/11/23 by Safronov, Oleg
#FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.1111.5552

Abstract

We consider a family of multi-dimensional Schrödinger operators -Δ+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,∞) for almost every t.

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