Communications in Mathematical Physics

, Volume 177, Issue 1, pp 221–254 | Cite as

Semiclassical study of quantum scattering on the line

  • Thierry Ramond


We study the well-known problem of 1-d quantum scattering by a potential barrier in the semiclassical limit. Using the so-called exact WKB method and semiclassical microlocal analysis techniques, we get a very precise and complete description of the scattering matrix, in particular when the energy is very close to a unique, quadratic maximum of the potential. In our one-dimensional setting, we also recover the Bohr-Sommerfeld quantization condition for the resonances generated by such a maximum.


Neural Network Statistical Physic Complex System Nonlinear Dynamics Quantization Condition 
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Copyright information

© Springer-Verlag 1996

Authors and Affiliations

  • Thierry Ramond
    • 1
  1. 1.Laboratoire Analyse Géométrie et Applications (URA CNRS 742)Université Paris NordVilletaneuseFrance

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