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Perturbation of embedded eigenvalues in the generalizedN-body problem

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Abstract

We discuss the perturbation of continuum eigenvalues without analyticity assumptions. Among our results, we show that generally a small perturbation removes these eigenvalues in accordance with Fermi's Golden Rule. Thus, generically (in a Baire category sense), the Schrödinger operator has no embedded non-threshold eigenvalues.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Hebrew University of Jerusalem, Israel

    Shmuel Agmon

  2. Department of Mathematics, University of Virginia, 22901, Charlottesville, Virginia, USA

    Shmuel Agmon & Ira Herbst

  3. Mathematics Institute, Aarhus University, Denmark

    Erik Skibsted

Authors
  1. Shmuel Agmon
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  2. Ira Herbst
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  3. Erik Skibsted
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Additional information

Communicated by B. Simon

Supported in part by NSF Grant DMS 8602826

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Agmon, S., Herbst, I. & Skibsted, E. Perturbation of embedded eigenvalues in the generalizedN-body problem. Commun.Math. Phys. 122, 411–438 (1989). https://doi.org/10.1007/BF01238435

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  • DOI: https://doi.org/10.1007/BF01238435

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