Multiple algebraisations of an elliptic Calogero-Sutherland model

Abstract

Recently, Gomez-Ullate et al. (1) have studied a particular N-particle quantum problem with an elliptic function potential supplemented by an external field. They have shown that the Hamiltonian operator preserves a finite dimensional space of functions and as such is quasi exactly solvable (QES). In this paper 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.

9 Revtex pages, 3 PS-figures; Summary, abstract and conclusions extended

References in corpus (1)

• Quasi Exactly Solvable NxN-Matrix Schroedinger Operators

Cited by in corpus (6)

• One-Dimensional Quasi-Exactly Solvable Schrödinger Equations
• Quasi-Exact Solvability and the direct approach to invariant subspaces
• sl(M+1) Construction of Quasi-solvable Quantum M-body Systems
• Quasi-exact-solvability of the $A_2/G_2$ Elliptic model: algebraic forms, $sl(3)/g^{(2)}$ hidden algebra, polynomial eigenfunctions
• The $B{C}_1$ Elliptic model: algebraic forms, hidden algebra $sl(2)$, polynomial eigenfunctions
• Quasi exactly solvable (QES) equations with multiple algebraisations