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Solvability of the G_2 Integrable System

Marcos Rosenbaum·Alexander Turbiner·Antonio Capella
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Abstract

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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BibTeXRIS

Marcos Rosenbaum, Alexander Turbiner, Antonio Capella. 1998-09-08. Solvability of the G_2 Integrable System. https://doi.org/10.1142/s0217751x98001815

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