Exactly solvable three-particle problem with three-body interaction

1996/12/31 by C. Quesne
Mathematics · Physics and Astronomy · #Combinatorics #Energy spectrum #Hamiltonian (control theory) #Many-body problem #Mathematical analysis #Mathematical physics #Mathematics #Nonlinear Waves and Solitons #Physics #Pure mathematics #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Quantum mechanics #Three-body problem #Trigonometry #Two-body problem #hep-th #math-ph #math.MP #n-body problem

paper · pdf · doi:10.1103/physreva.55.3931

published as Phys.Rev. A55 (1997) 3931-3934 · LaTeX, 15 pages, no figures, slightly shortened version to appear in Phys. Rev. A, one error corrected

openalex publication_date 1997/05/01 · arxiv created 1997/05/13 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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 symmetric polynomials. The exact solvability of the problem with three-body interaction is explained by a hidden sl(3,R) symmetry.

Citations

• EXACT SOLVABILITY OF THE CALOGERO AND SUTHERLAND MODELS
• Solution of the One-Dimensional N-Body Problems with Quadratic and/or Inversely Quadratic Pair Potentials
• Interacting Fermion Systems from Two Dimensional QCD
• Dynamical correlation functions in the Calogero-Sutherland model
• Some combinatorial properties of Jack symmetric functions