`Slow' variable discretization: a novel approach for Hamiltonians allowing adiabatic separation of variables

Abstract

We propose a novel approach for Hamiltonians allowing adiabatic separation of variables. Our method is based on the assumption of smoothness of the motion associated with the adiabatic variable instead of its slowness, which is assumed traditionally. Convergence in terms of the number of coupled channels in our method corresponds to the standard adiabatic expansion. However, neither laborious calculations of non-adiabatic couplings nor a priori information on locations of avoided crossings are required. The method is illustrated by calculating bound-state energies for several three-body Coulomb systems for states with zero total angular momentum.