Pseudotime Schrodinger equation with absorbing potential for quantum scattering calculations

The Schrodinger equation (H psi)(r) = [E + u(E)W(r)]psi (r) With an energy- dependent complex absorbing potential -u(E)W(r), associated with a scatteri ng system, can be reduced for a special choice of u(E) to a harmonic invers ion problem of a discrete pseudotime correlation function y(t) = phi (T)U(t )phi. An efficient formula for Greens function matrix elements is also deri ved. Since the exact propagation up to time 2t can be done with only simila r tot real matrix-vector products, this gives an unprecedently efficient sc heme for accurate calculations of quantum spectra for possibly very large s ystems.