Canonical transformation approach to the linear Jahn–Teller effect E–e

Abstract

An analytical approach is presented for the linear Jahn–Teller effect E–e. This approach yields analytical expressions for both the ground state and the lowest five excited states over the weak and intermediate coupling range (0?k²?3). The method is based on canonical transformations combined with perturbation theory. A comparison of our results with existing numerical solutions to this problem shows good agreement within the weak and intermediate coupling range. Ham’s reduction factors p and q as well as the oscillating behavior of the energy levels for large quantum number n are also discussed.