Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1997-06-10
in Calogero-Moser Sutherland Models, eds. J.F. van Diejen and L. Vinet (Springer-Verlag, New York, 2000) pp. 411-420
Physics
High Energy Physics
High Energy Physics - Theory
10 pages, LaTeX, no figures, communication at the Workshop on Calogero-Moser-Sutherland Models, Montreal, March 10-15, 1997 (t
Scientific paper
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.
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