A time-independent wavepacket approach to the (t,t')-method for treating time-dependent Hamiltonian systems

We derive the appropriate ''time-independent wavepacket'' (TIW) form of the Schrodinger 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. (C) 1997 Elsevier Science B.V.