Ionization and excitation of the hydrogen atom by an electric pulse

We investigate the excitation and ionization of the hydrogen atom using an electric pulse of both Gaussian and rectangular shape. The time-dependent Schrodinger equation is solved numerically using the discrete variable representation. In the regime where the pulse duration corresponds to almost adiabatic evolution of the system, an estimate of the probability for inelastic processes based on advanced adiabatic theory is in good agreement with numerical results.