Non-adiabatic corrections for coupled oscillators using Rayleigh-Schrödinger perturbation theory

Abstract

An adiabatic separation is applied to two coupled oscillators described by the generalized Henon-Heiles hamiltonian, and to a system with the coupling term of the form x ² y ². The resulting approximate quantum mechanical energies are corrected for non-adiabatic interactions by perturbation theory. The convergence properties of the perturbation series are demonstrated for different harmonic frequencies and magnitude of perturbation. The order in which the adiabatic separation is made is shown to have little effect on the accuracy of the energy levels.