Relative performances of the Kohn, Schwinger, and Newton variational principles in scattering theory
B. Ramachandran, Tai-Guang Wei, Róbert E. Wyatt · The Journal of Chemical Physics · 1988
Comparisons of three variational principles commonly used in scattering problems, namely those due to Kohn (KVP), Schwinger (SVP), and Newton (NVP), are presented. These comparisons are conducted by computing K-matrix elements for elastic scattering from nine different interaction potentials. We represent the KVP trial functions as expansions containing two non-L2 terms that represent the asymptotic free wave, and a set of L2 functions, while the SVP and the NVP trial functions are expansions containing only the L2 terms. Three different sets of L2 functions are used to examine the effect of changing the basis on the convergence characteristics of the three methods. We find that the rates of convergence for the Kohn, Schwinger, and Newton methods are strongly dependent on the nature of the potential and the basis set used. We also find that purely repulsive potentials are, in general, easier to converge than purely attractive potentials.