Quasi-exact-solution of the generalized E ⊗ ε Jahn-Teller Hamiltonian

We consider the solution of a generalized E circle times epsilon 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.