Pseudotime Schrödinger equation with absorbing potential for quantum scattering calculations.

The Schrödinger equation (Hpsi) (r) = [E+u(E)W(r)]psi(r) with an energy-dependent complex absorbing potential -u(E)W(r), associated with a scattering system, can be reduced for a special choice of u(E) to a harmonic inversion problem of a discrete pseudotime correlation function y(t) = phi(T)U(t)phi. An efficient formula for Green's function matrix elements is also derived. Since the exact propagation up to time 2t can be done with only approximately t real matrix-vector products, this gives an unprecedently efficient scheme for accurate calculations of quantum spectra for possibly very large systems.