An exactly solvable three-particle problem with three-body interaction

Abstract

The energy spectrum of 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 derived. When expressed in appropriate variables, the corresponding wave functions are shown to be expressible in terms of Jack polynomials. The exact solvability of the problem with three-body interaction is explained by a hidden sl(3,\R) symmetry.

LaTeX, 15 pages, no figures, slightly shortened version to appear in Phys. Rev. A, one error corrected

References in corpus (6)

• Exact Solvability of the Calogero and Sutherland Models
• Dynamical correlation functions in the Calogero-Sutherland model
• Interacting Fermion Systems from Two Dimensional QCD
• Multicomponent Calogero Model of $B_N$-Type Confined in Harmonic Potential
• Exchange operators and extended Heisenberg algebra for the three-body Calogero-Marchioro-Wolfes problem
• Three-body generalization of the Sutherland model with internal degrees of freedom

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• Superintegrable 3-body systems on the line
• Solvable three boson model with attractive delta function interactions
• sl(M+1) Construction of Quasi-solvable Quantum M-body Systems
• Extending the four-body problem of Wolfes to non-translationally invariant interactions
• Solvable few-body quantum problems
• Symmetries of Spin Calogero Models
• Exactly solvable $N$-body quantum systems with $N=3^k(k\ge 2)$ in the $D=1$ dimensional space