Action-angle variables for quantum mechanical coplanar scattering

A formulation of quantum mechanical scattering is presented with action-angle variables. The theory is confined to coplanar three atom scattering which reduces to the consideration of three coordinates taking into account conservation of energy and angular momentum. The resultant partial differential equation is treated within a finite element formulation with the spatial elements taken as parallelopipeds. It is argued that the choice of the three independent coordinates in a calculation is not critical and no channel matching is required, although it could be included. A simple illustration with rotationally inelastic scattering is considered for the H+H₂ system. The results are in good agreement with earlier close coupling calculations.