Multiple algebraisations of an elliptic Calogero-Sutherland model. (English) Zbl 1063.81063
Summary: Recently, D. Gómez-Ullate et al. [Phys. Lett. B 511, No. 1, 112–118 (2001; Zbl 1062.81518)] 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.
MSC:
| 81R12 | Groups and algebras in quantum theory and relations with integrable systems |
| 33E05 | Elliptic functions and integrals |
Citations:
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