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)


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.


Point Spectrum Semiclassical Limit Shape Resonance Resonant Energy Pure Point Spectrum 
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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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