Exact Solution of the Quantum Calogero-Gaudin System and of its q-Deformation

Abstract

A complete set of commuting observables for the Calogero-Gaudin system is diagonalized, and the explicit form of the corresponding eigenvalues and eigenfunctions is derived. We use a purely algebraic procedure exploiting the co-algebra invariance of the model; with the proper technical modifications this procedure can be applied to the $q-$deformed version of the model, which is then also exactly solved.

20 pages Latex

References in corpus (4)

• A systematic construction of completely integrable Hamiltonians from coalgebras
• Generating function of correlators in the sl_2 Gaudin model
• Integrable deformations of Hamiltonian systems and q-symmetries
• Two-photon algebra deformations

Cited by in corpus (11)

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• The spin 1/2 Calogero-Gaudin System and its q-Deformation
• Coupling coefficients of $s{u}_q(1,1)$ and multivariate $q$-Racah polynomials
• Gaudin models with ${\CU}_q(\mathfrak{osp}(1 | 2))$ symmetry
• Superintegrable Deformations of the Smorodinsky-Winternitz Hamiltonian
• An infinite family of Dunkl type superintegrable curved Hamiltonians through coalgebra symmetry: Oscillator and Kepler-Coulomb models
• Quantum group deformation of the Kittel--Shore model
• Exact solution of a supersymmetric Gaudin model