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A complete set of commuting observables for the Calogero-Gaudin system isdiagonalized, and the explicit form of the corresponding eigenvalues andeigenfunctions is derived. We use a purely algebraic procedure exploiting theco-algebra invariance of the model; with the proper technical modificationsthis procedure can be applied to the $q-$deformed version of the model, whichis then also exactly solved.Comment: 20 pages Late

Exact solution of the quantum Calogero–Gaudin system and of its q deformation