Absolutely continuous spectrum of a one-parameter family of Schrödinger operators

Safronov, O.

doi:10.1090/S1061-0022-2013-01275-1

Absolutely continuous spectrum of a one-parameter family of Schrödinger operators
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by O. Safronov

St. Petersburg Math. J. 24 (2013), 977-989

DOI: https://doi.org/10.1090/S1061-0022-2013-01275-1

Published electronically: September 23, 2013

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Abstract:

Under certain conditions on the potential $V$, it is shown that the absolutely continuous spectrum of the Schrödinger operator $-\Delta +\alpha V$ is essentially supported on $[0,+\infty )$ for almost every $\alpha \in \mathbb R$.

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