Symmetry of Jahn-Teller systems and their solvability

Abstract:
We present a method of obtaining the quasi exact solution of the Jahn Teller systems in the framework of osp(2,2) superalgebra. The hamiltonian have been solved in the Bargmann-Fock space by obtaining an expression as linear and bilinear combinations of the generators of osp(2,2).  In particulare, we have discussed quasi exact solvability of $E \times E$  Jahn-Teller Hamiltonian.