Treatment of the generalised E × ϵ Jahn-Teller Hamiltonian in polar coordinates

Abstract

The generalised E* epsilon Jahn-Teller Hamiltonian is treated in configuration space using polar coordinates. The expansion in radial oscillator states leads to simple recurrence relations. These are equivalent to a system of two ordinary linear first-order differential equations. The isolated exact solutions are polynomials multiplied with an exponential function in this formulation. They are also calculated in configuration space. The connection of the present treatment with Reik's treatment is established. This leads to a new understanding of Reik's Neumann series expansion.