English

Explicit solution of the quantum three-body Calogero-Sutherland model

High Energy Physics - Theory 2009-10-31 v1 Exactly Solvable and Integrable Systems solv-int

Abstract

Quantum integrable systems generalizing Calogero-Sutherland systems were introduced by Olshanetsky and Perelomov (1977). Recently, it was proved that for systems with trigonometric potential, the series in the product of two wave functions is a deformation of the Clebsch-Gordan series. This yields recursion relations for the wave functions of those systems. In this note, this approach is used to compute the explicit expressions for the three-body Calogero-Sutherland wave functions, which are the Jack polynomials. We conjecture that similar results are also valid for the more general two-parameters deformation introduced by Macdonald.

Keywords

Cite

@article{arxiv.hep-th/9805149,
  title  = {Explicit solution of the quantum three-body Calogero-Sutherland model},
  author = {A. M. Perelomov and E. Ragoucy and P. Zaugg},
  journal= {arXiv preprint arXiv:hep-th/9805149},
  year   = {2009}
}

Comments

10 pages

R2 v1 2026-07-22T16:10:34.138Z