Multiple algebraisations of an elliptic Calogero-Sutherland model

Details Multiple algebraisations of an elliptic Calogero-Sutherland model Multiple algebraisations of an elliptic Calogero-Sutherland model

2002-05-09

arxiv.org/abs/quant-ph/0205046v2

J.Math.Phys.44:1576,2003

Physics

Quantum Physics

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

Scientific paper

10.1063/1.1557788

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.

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