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.
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