ANALYTIC CONTINUATION OF THE POLYNOMIAL REPRESENTATION OF THE FULL, INTERACTING TIME-INDEPENDENT GREEN-FUNCTION

We present an analytic continuation of a polynomial representation of the full, interacting time-independent Green function, thereby enabling the use of negative, imaginary absorbing potentials to shorten the grid necessary to treat scattering problems. The approach retains the clean separation of the energy and Hamiltonian dependences characteristic of our earlier orthogonal polynomial representation of the operator (E-H+i0+)-1. This treatment, combined with our time-independent wavepacket Lippmann-Schwinger equation method, leads to a computational approach in which all of the energy dependence resides in known analytical expansion coefficients. The Hamiltonian operator appears as the argument of other orthogonal polynomials. These act solely on an initial wavepacket which provides a ''universal source'' of scattered waves, independent of the particular energies of interest. This energy independence, combined with highly truncated grids, results in an extremely efficient procedure for scattering calculations.