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

Details Absolutely continuous spectrum of a one-paramentric family of Schrödinger operators Absolutely continuous spectrum of a one-paramentric family of Schrödinger operators

2011-06-09

arxiv.org/abs/1106.1712v5

Mathematics

Spectral Theory

Scientific paper

We consider a family of operators $-\Delta+ t V$ with a slowly decaying and
oscillating potential $V$. We prove that the absolutely continuous spectrum of
this operator is essentially supported by $[0,\infty)$ for almost every $t$.

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