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Communications in Mathematical Physics

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

Semiclassical study of quantum scattering on the line

  • Thierry Ramond
Article

Abstract

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.

Keywords

Neural Network Statistical Physic Complex System Nonlinear Dynamics Quantization Condition 
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 1996

Authors and Affiliations

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

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