Parabolic wave packets for time propagation of atomic hydrogen in an electric field of short laser pulses

We propose parabolic wave packets (PWP) as trial functions to solve the time-dependent Schrodinger equation (TDSE) for atomic hydrogen in a short laser pulse. Within the framework of the time-dependent variational principle, the TDSE is transformed into a set of first-order differential equations for the parameters of the wave packets. Thanks to the asymptotic properties of the PWP, the ionization amplitude is expressed in closed form in terms of the wave packets' parameters. The robustness of the method is first validated with a test model with analytical solution and then applied to the ionization process of atomic hydrogen in half- and few-cycle laser pulses. The results compare very well with those obtained with other approaches.