Quasi-exact-solution of the Generalized Exe Jahn-Teller Hamiltonian

We consider the solution of a generalized Exe Jahn-Teller Hamiltonian in the context of quasi-exactly solvable spectral problems. This Hamiltonian is expressed in terms of the generators of the osp(2,2) Lie algebra. Analytical expressions are obtained for eigenstates and eigenvalues. The solutions lead to a number of earlier results discussed in the literature. However, our approach renders a new understanding of ``exact isolated'' solutions.