Variational expressions for first-order properties involving continuum wave functions

We discuss methods for computing first-order matrix elements involving continuum wave functions variationally. Specifically, we show that the trial wave function obtained from the Kohn method will give a variational result for any first-order property. We also discuss a variational technique for computing the squared modulus of a first-order matrix element based on approximating the resolvent. We explain why the resolvent method will converge more slowly in certain cases and illustrate our remarks with calculations on a model problem