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

Safronov, Oleg

doi:10.1090/S0002-9939-2013-12186-6

Absolutely continuous spectrum of a typical Schrödinger operator with a slowly decaying potential
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Proc. Amer. Math. Soc. 142 (2014), 639-649 Request permission

Abstract:

We study a family of Schrödinger operators $-{\Delta }+\alpha V$. We find conditions on $V$ that guarantee that the a.c. spectrum of the operator covers the interval $[0,\infty )$ for almost every $\alpha$.

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