Explicit solution of the quantum three-body Calogero-Sutherland model

Abstract

Quantum integrable systems generalizing Calogero-Sutherland systems were introduced by Olshanetsky and Perelomov (1977). Recently, it was proved that for systems with trigonometric potential, the series in the product of two wave functions is a deformation of the Clebsch-Gordan series. This yields recursion relations for the wave functions of those systems. In this note, this approach is used to compute the explicit expressions for the three-body Calogero-Sutherland wave functions, which are the Jack polynomials. We conjecture that similar results are also valid for the more general two-parameters deformation introduced by Macdonald.

10 pages

Cited by in corpus (10)

• An elementary construction of lowering and raising operators for the trigonometric Calogero-Sutherland model
• On an approach for computing the generating functions of the characters of simple Lie algebras
• Quantum trigonometric Calogero-Sutherland model, irreducible characters and Clebsch-Gordan series for the exceptional algebra E7
• $\mathcal{P}\mathcal{T}$ deformation of Calogero-Sutherland models
• Some results on the eigenfunctions of the quantum trigonometric Calogero-Sutherland model related to the Lie Algebra $D_4$
• Some results on the eigenfunctions of the quantum trigonometric Calogero-Sutherland model related to the Lie algebra E6
• The generating function for a particular class of characters of SU(n)
• Algebraic Exact Solvability of trigonometric-type Hamiltonians associated to root systems
• Algebraic integrability of $\mathcal{P}\mathcal{T}$-deformed Calogero models
• An Analytic Formula for the A_2 Jack Polynomials