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)


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.


Cauchy Problem Schrodinger Equation Sobolev Type Canonical Commutation Relation Dunkl Operator 
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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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