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The shape resonance

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Abstract

For a class of Schrödinger operatorsH:=−(ℏ2/2m)Δ+V onL 2(ℝn), with potentials having minima embedded in the continuum of the spectrum and non-trapping tails, we show the existence of shape resonances exponentially close to the real axis as ℏ↘0. The resonant energies are given by a convergent perturbation expansion in powers of a parameter exhibiting the expected exponentially small behaviour for tunneling.

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Authors and Affiliations

  1. Centre de Physique Théorique, CNRS — Luminy — Case 907, F-13288, Marseille Cedex 9, France

    J. M. Combes, P. Duclos, M. Klein & R. Seiler

  2. PHYMAT, Department de Mathématique, Université de Toulon et du Var, France

    J. M. Combes, P. Duclos, M. Klein & R. Seiler

  3. Fachbereich Mathematik, Technische Universität Berlin, D-1000, Berlin 12

    J. M. Combes & P. Duclos

  4. Laboratoire propre du Centre national de la recherche scientifique, France

    M. Klein & R. Seiler

Authors
  1. J. M. Combes
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  2. P. Duclos
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  3. M. Klein
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  4. R. Seiler
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Communicated by B. Simon

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Combes, J.M., Duclos, P., Klein, M. et al. The shape resonance. Commun.Math. Phys. 110, 215–236 (1987). https://doi.org/10.1007/BF01207364

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  • DOI: https://doi.org/10.1007/BF01207364

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