On variational principles in scattering theory using discontinuous trial functions

The usual variational principles employed in scattering calculations are only valid provided that the trial functions used are continuous and have continuous first derivatives. Since it is not the wave function itself that is required but rather the quantities which relate to the calculation of cross sections, it may be desirable to use discontinuous functions, in which case the usual variational principles must be altered. Variational expressions are therefore presented for the scattering amplitudes and for the R matrix which are valid for e-H scattering using a particular class of discontinuous trial functions.