Multiple algebraisations of an elliptic Calogero–Sutherland model

Abstract

Recently, Gómez-Ullate et al. [Phys. Lett. B 511, 112 (2001)] have studied an N-particle quantum problem with elliptic-function potentials. They have shown that the Hamiltonian operator preserves a finite dimensional space of functions and as such is quasi-exactly solvable (QES). In this article we show that other types of invariant function spaces exist, which are in close relation to the algebraic properties of the elliptic functions. Accordingly, series of new algebraic eigenfunctions can be constructed.