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

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.