A collocation approach for quantum scattering based on the S-matrix version of the Kohn variational principle

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Abstract
A collocation approach to quantum scattering is presented. The method is based on the S‐matrix version of the Kohn variational principle with a different linear expansion used for the two wave functions—one is a linear combination of basis functions and the other is a pointwise representation with proper asymptotic conditions imposed. The resulting equations are similar in structure to the usual version of the Kohn variational principle, however, in the present approach there are no integrals between the square integrable (L2) basis functions. In addition, the method does not require the knowledge of quadrature weights associated with the collocation points as was the case in a previous pointwise method for quantum scattering. This property means that the method is readily applicable to reactive scattering problems which use different sets of coordinates for reactants and products. Appliction to a simple inelastic test problem (collinear He–H2 vibrationally inelastic scattering) shows the accuracy of the approach to be comparable to that of the usual variatinal form of the S‐matrix Kohn method.