An explicit solution of the (quantum) elliptic Calogero-Sutherland model

Abstract

We present explicit formulas for the eigenvalues and eigenfunctions of the elliptic Calogero-Sutherland (eCS) model as formal power series to all orders in the nome of the elliptic functions, for arbitrary values of the (positive) coupling constant and particle number. Our solution gives explicit formulas for an elliptic deformation of the Jack polynomials.

16 pages, Contribution to SPT 2004 in Cala Gonone (Sardinia, Italy) v2 and v3: minor corrections

Cited by in corpus (5)

• On Elliptic Algebras and Large-n Supersymmetric Gauge Theories
• Combinatorial approach to Mathieu and Lamé equations
• Eigenproblem for Jacobi matrices: hypergeometric series solution
• Exact quantization conditions for the elliptic Ruijsenaars-Schneider model
• A new treatment for some periodic Schrödinger operators II: the wave function