The Calogero-Sutherland Model and Generalized Classical Polynomials

Details The Calogero-Sutherland Model and Generalized Classical Polynomials The Calogero-Sutherland Model and Generalized Classical Polynomials

1996-08-12

arxiv.org/abs/solv-int/9608004v1

Commun.Math.Phys. 188 (1997) 175-216

Physics

High Energy Physics

High Energy Physics - Theory

LaTeX 2.09, 41 pages, uses subeqnarray.sty

Scientific paper

10.1007/s002200050161

Multivariable generalizations of the classical Hermite, Laguerre and Jacobi polynomials occur as the polynomial part of the eigenfunctions of certain Schr\"odinger 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.

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