Green's functions for separable potentials

Summary The convergence properties of approximate one-particle Green's functions derived from separable potential expansions are examined. A convergence criterion for the basis set to be used in a Löwdin-type inner projection is established and illustrated by calculations of matrix elements of the Coulomb Green's function based on separable potentials of finite rank. It is then suggested that a separable potential ansatz for a many-electron wave function may be introduced into Frenkel's time-dependent variation principle in order to obtain approximate response functions with the continuum of one-particle states explicitly included. A preliminary outline of the formalism at the time-dependent Hartree-Fock level is presented.