Iterative solution in quantum scattering theory. The log derivative Kohn approach

TLDR: In this article, the log derivative version of the Kohn variational principle is reviewed in the context of a general inelastic molecular collision, and the possibility of solving the resulting linear equations iteratively for a single initial state column of the scattering matrix, S, is made.

Abstract: The log derivative version of the Kohn variational principle is reviewed in the context of a general inelastic molecular collision. Particular emphasis is placed on the possibility of solving the resulting linear equations iteratively for a single initial state column of the scattering matrix, S, and several important practical observations are made in this regard. In particular, it is argued that the discrete variable representation proposed by Light and coworkers leads to an extremely sparse coefficient matrix, and so has distinct advantages over the more obvious variational basis approach. The resulting methodology is applied to the diffractive scattering of a beam of helium atoms from the (001) face of LiF. Here test calculations with up to 2601 coupled channels and 216 translational grid points clearly demonstrate the practical potential of the iterative technique. The implications of these tests for more general scattering problems are also briefly discussed.