A time-independent wavepacket approach to the ( t, t′)-method for treating time-dependent Hamiltonian systems

Abstract

We derive the appropriate “time-independent wavepacket” (TIW) form of the Schrödinger equation governing collisions involving a time-dependent interaction. This is done using the ( t, t′)-method, whereby the time-dependence is treated like an additional spatial variable, t′, and a quasi-time, t, is introduced of which the Hamiltonian is independent. The TIW equation is solved numerically by a Chebyshev expansion method which separates dependence on the initial energy from dependence on the Hamiltonian. This results in a very efficient computational procedure which we illustrate by application to scattering through an oscillating square-barrier potential.