Pseudotime Schrödinger Equation with Absorbing Potential for Quantum Scattering Calculations

The Schrödinger equation \(Hψ\) \(r\) = [E+u_EW\(r\)]ψ\(r\) with an energy-dependent complex absorbing potential -u_EW\(r\), 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\(t\) = φ^TU^tφ. 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 ~t real matrix-vector products, this gives an unprecedently efficient scheme for accurate calculations of quantum spectra for possibly very large systems.