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On the shape resonance

  • J. M. Combes
  • P. Duclos
  • R. Seiler
II Mathematical Framework
Part of the Lecture Notes in Physics book series (LNP, volume 211)

Abstract

We computed poles of the S-matrix as the poles of some expectation values of the resolvent through a perturbation by a Dirichlet boundary condition. They are exponentially close to the real axis. Our results are valid if k is small (large masses, quasiclassical regime).

The perturbation theory is based upon the equation rч = r ч D + πч.

The resonant energies are given in terms of a convergent power series expansion in the tunneling parameter t. This parameter is exponentially small in k−2.

Keywords

Point Spectrum Semiclassical Limit Shape Resonance Resonant Energy Pure Point Spectrum 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1984

Authors and Affiliations

  • J. M. Combes
    • 1
  • P. Duclos
    • 1
  • R. Seiler
    • 2
  1. 1.Université de Toulon et du Var and Centre de Physique ThéoriqueCNRSMarseille Cedex 9France
  2. 2.Fachbereich MathematikTechnische Universität BerlinBerlin 12

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