SLOW VARIABLE DISCRETIZATION - A NOVEL-APPROACH FOR HAMILTONIANS ALLOWING ADIABATIC SEPARATION OF VARIABLES

We propose a novel approach for Hamiltonians allowing adiabatic separa tion of variables. Our method is based on the assumption of smoothness of the motion associated with the adiabatic variable instead of its s lowness, which is assumed traditionally. Convergence in terms of the n umber of coupled channels in our method corresponds to the standard ad iabatic expansion. However, neither laborious calculations of non-adia batic couplings nor a priori information on locations of avoided cross ings are required. The method is illustrated by calculating bound-stat e energies for several three-body Coulomb systems for states with zero total angular momentum.