Explicit solution of the (quantum) elliptic Calogero-Sutherland model

Details Explicit solution of the (quantum) elliptic Calogero-Sutherland model Explicit solution of the (quantum) elliptic Calogero-Sutherland model

2004-01-14

arxiv.org/abs/math-ph/0401029v3

Physics

Mathematical Physics

v1: 17 pages. The solution is given as series in q but only to low order. v2: 30 pages. Results significantly extended. v3: 35

Scientific paper

We derive explicit formulas for the eigenfunctions and eigenvalues of the elliptic Calogero-Sutherland model as infinite series, to all orders and for arbitrary particle numbers and coupling parameters. The eigenfunctions obtained provide an elliptic deformation of the Jack polynomials. We prove in certain special cases that these series have a finite radius of convergence in the nome $q$ of the elliptic functions, including the two particle (= Lam\'e) case for non-integer coupling parameters.

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