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

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

1998-05-22

arxiv.org/abs/hep-th/9805149v1

J.Phys. A31 (1998) L559-L565

Physics

High Energy Physics

High Energy Physics - Theory

10 pages

Scientific paper

10.1088/0305-4470/31/32/002

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.

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