Three-body Generalizations of the Sutherland Problem
Quesne, C.
arXiv, 9706067 / Harvested from arXiv
Text on arXiv
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 $sl(3,R)$ 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~$D_6$. Three alternative commuting operators are also introduced.
Publié le : 1997-06-10
Classification:  High Energy Physics - Theory,  Mathematical Physics,  Nonlinear Sciences - Exactly Solvable and Integrable Systems 
@article{9706067,
     author = {Quesne, C.},
     title = {Three-body Generalizations of the Sutherland Problem},
     journal = {arXiv},
     volume = {1997},
     number = {0},
     year = {1997},
     language = {en},
     url = {http://dml.mathdoc.fr/item/9706067}
}

Quesne, C. Three-body Generalizations of the Sutherland Problem. arXiv, Tome 1997 (1997) no. 0, . http://gdmltest.u-ga.fr/item/9706067/