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The Calogero-Moser Model, the Calogero Model and Analytic Extension

  • Shuji Watanabe
Part of the International Society for Analysis, Applications and Computation book series (ISAA, volume 9)

Abstract

The Calogero-Moser model, the Calogero model and the Sutherland model describe quantum integrable particle systems with long-range interactions and have attracted considerable interest. We explicitly give the solution of the Cauchy problem for the two-body problem of each of the Calogero-Moser model and the Calogero model. To this end we regard the solution u(t, ·) as an analytic function of time t and construct both a generalized Fourier cosine transform and a generalized Fourier sine transform. Moreover, we show an embedding theorem of Sobolev type as another application of these transforms.

Keywords

Cauchy Problem Schrodinger Equation Sobolev Type Canonical Commutation Relation Dunkl Operator 
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 Science+Business Media Dordrecht 2001

Authors and Affiliations

  • Shuji Watanabe
    • 1
  1. 1.Department of Electronics and Information EngineeringAichi University of TechnologyNishihazama-cho, GamagouriJapan

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