The shape resonance |
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| Authors: | J. M. Combes P. Duclos M. Klein R. Seiler |
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| Affiliation: | (1) Centre de Physique Théorique, CNRS — Luminy — Case 907, F-13288 Marseille Cedex 9, France;(2) PHYMAT, Department de Mathématique, Université de Toulon et du Var, France;(3) Fachbereich Mathematik, Technische Universität Berlin, D-1000 Berlin 12;(4) Laboratoire propre du Centre national de la recherche scientifique, France |
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| Abstract: | For a class of Schrödinger operatorsH:=–( 2/2m) +V onL2( n), 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  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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