  A global solution of the Schr\"odinger equation for explicitly time-dependent
Hamiltonians is derived by integrating the non-linear differential equation
associated with the time-dependent wave operator. A fast iterative solution
method is proposed in which, however, numerous integrals over time have to be
evaluated. This internal work is done using a numerical integrator based on
Fast Fourier Transforms (FFT). The case of a transition between two potential
wells of a model molecule driven by intense laser pulses is used as an
illustrative example. This application reveals some interesting features of the
integration technique. Each iteration provides a global approximate solution on
grid points regularly distributed over the full time propagation interval.
Inside the convergence radius, the complete integration is competitive with
standard algorithms, especially when high accuracy is required.
