Communications in Mathematical Physics

, Volume 188, Issue 1, pp 175–216 | Cite as

The Calogero-Sutherland Model and Generalized Classical Polynomials

  • T.H. Baker
  • P.J. Forrester


Multivariable generalizations of the classical Hermite, Laguerre and Jacobi polynomials occur as the polynomial part of the eigenfunctions of certain Schrödinger operators for Calogero-Sutherland-type quantum systems. For the generalized Hermite and Laguerre polynomials the multidimensional analogues of many classical results regarding generating functions, differentiation and integration formulas, recurrence relations and summation theorems are obtained. We use this and related theory to evaluate the global limit of the ground state density, obtaining in the Hermite case the Wigner semi-circle law, and to give an explicit solution for an initial value problem in the Hermite and Laguerre case.


Quantum System Recurrence Relation Classical Result State Density Explicit Solution 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • T.H. Baker
    • 1
  • P.J. Forrester
    • 2
  1. 1.Department of Mathematics, University of Melbourne, Parkville, Victoria 3052, Australia.¶E-mail:
  2. 2. Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606, JapanJP

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