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On the Absolutely Continuous Spectrum of Multi-Dimensional Schrödinger Operators with Slowly Decaying Potentials

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Abstract

We consider a multi-dimensional Schrödinger operator −Δ+V in L2(Rd) and find conditions on the potential V which guarantee that the absolutely continuous spectrum of this operator is essentially supported by the positive real line. We prove some results which go beyond the case L1+Lp with p<d.

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Authors and Affiliations

  1. Department of Mathematics, UAB, 1300 University Boulevard, Birmingham, AL, 35294, USA

    Oleg Safronov

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  1. Oleg Safronov
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Correspondence to Oleg Safronov.

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Communicated by B. Simon

The author is grateful to Gunter Stolz for useful discussions. The work was supported by the grant of NSF DMS-0245210.

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Safronov, O. On the Absolutely Continuous Spectrum of Multi-Dimensional Schrödinger Operators with Slowly Decaying Potentials. Commun. Math. Phys. 254, 361–366 (2005). https://doi.org/10.1007/s00220-004-1161-0

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  • DOI: https://doi.org/10.1007/s00220-004-1161-0

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