A comparison between R-matrix and variational procedures

A class of variational methods that can be used in solving either bound state problems or those that involve scattering by a potential is reviewed with particular regard to the constraints that it is necessary to impose upon the basis functions. The R-matrix method is also reviewed and it is shown that there is a formal similarity between the two methods but that the basis functions of the R-matrix method are excluded as a basis for the variational procedure. As a result, the convergence properties of the two methods differ, the variational procedures converge rapidly but the R-matrix method needs a 'correction' to improve the convergence. The relations between the variational procedures discussed and two other methods, one due to Kohn (1948) and one due to Rudge (1973), are also mentioned