In this paper, we propose a supersymmetric SU (1|2) Gaudin model and have derived its eigenvalues. We also present the well-defined eigenstates through the quasi-classical limit of the eigenstates in the supersymmetric t-J model.
A special case of the Gaudin model related to the superalgebra osp(1,2) is investigated. An exact solution for the model in the spin-1/2 representation is presented. A complete set of commuting observables is diagonalized and the corresponding eigenvectors and eigenvalues are explicitly calculated. The approach used in this paper is based on the co-algebra symmetry of the model, already known from the spin-1/2 Calogero-Gaudin system.