THE CANONICAL FORM OF THE E-CIRCLE-TIMES-EPSILON JAHN-TELLER HAMILTONIAN

The E x epsilon Jahn-Teller Hamiltonian in its Bargmann-Fock represent ation is transformed by the Birkhoff method into a canonical form in w hich all regular singularities between zero and infinity have been rem oved. The resulting equation is of the Kummer type and identical to th e previously obtained canonical form of the Rabi Hamiltonian (Szopa M and Ceulemans A 1996 J. Math. Phys. 37 5402). The isolated exact solut ions of the E x beta, E x epsilon and Gamma(8)x tau(2) Jahn-Teller Ham iltonians are identified as special symmetries of the canonical form.