Solvability of the G_2 Integrable System

Details Solvability of the G_2 Integrable System Solvability of the G_2 Integrable System

1997-07-07

arxiv.org/abs/solv-int/9707005v4

Int.J.Mod.Phys. A13 (1998) 3885-3904

Physics

Condensed Matter

18 pages, LaTeX, some minor typos corrected

Scientific paper

10.1142/S0217751X98001815

It is shown that the 3-body trigonometric G_2 integrable system is exactly-solvable. If the configuration space is parametrized by certain symmetric functions of the coordinates then, for arbitrary values of the coupling constants, the Hamiltonian can be expressed as a quadratic polynomial in the generators of some Lie algebra of differential operators in a finite-dimensional representation. Four infinite families of eigenstates, represented by polynomials, and the corresponding eigenvalues are described explicitly.

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