Variational study for the ground state energy of the linear E–b1, b2 Jahn–Teller system

A new method for determining the ground state wave functions of the linear E–b1, b2 Jahn–Teller system is presented. Up to now all methods for determining the ground state wave functions lead to relatively large errors in determining the ground state energies of the linear E–e Jahn–Teller system in comparison with the exact diagonalization results. The presented method is based on a combination of unitary transformations and the variational principle, and the results of this method are presented on the linear E–e Jahn–Teller system. The ground state energies calculated by the ground state wave functions obtained by the presented method are in very good agreement with the exact diagonalization results and are substantially better than those from earlier studies. This method uses a linear combination of displacements of a vacuum state which can be considered as generalization of a two-mode squeezed vacuum state defined in the earlier studies. Further, this method is used to prove that the ground state energy of the linear E–b1, b2 Jahn–Teller system is twofold degenerate. This method provides not only the analytical ground state wave functions for the linear E–e Jahn–Teller system examined in the previous studies but also for the linear E–b1, b2 Jahn–Teller system which is more general than the linear E–e Jahn–Teller system.