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

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 $[0,\infty)$ for almost every $t$.

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