Three-body Generalizations of the Sutherland Problem
Abstract
The three-particle Hamiltonian obtained by replacing the two-body trigonometric potential of the Sutherland problem by a three-body one of a similar form is shown to be exactly solvable. When written in appropriate variables, its eigenfunctions can be expressed in terms of Jack symmetric polynomials. The exact solvability of the problem is explained by a hidden symmetry. A generalized Sutherland three-particle problem including both two- and three-body trigonometric potentials and internal degrees of freedom is then considered. It is analyzed in terms of three first-order noncommuting differential-difference operators, which are constructed by combining SUSYQM supercharges with the elements of the dihedral group~. Three alternative commuting operators are also introduced.
Keywords
Cite
@article{arxiv.hep-th/9706067,
title = {Three-body Generalizations of the Sutherland Problem},
author = {C. Quesne},
journal= {arXiv preprint arXiv:hep-th/9706067},
year = {2008}
}
Comments
10 pages, LaTeX, no figures, communication at the Workshop on Calogero-Moser-Sutherland Models, Montreal, March 10-15, 1997 (to be published in the Proceedings)