  We investigate the Rydberg states generation of Hydrogen atoms with intense
laser pulses, by solving the time-dependent Schr\"odinger equation and by means
of classical trajectory monte-carlo simulations. Both linearly polarized
multi-cycle pulses and pairs of optical half cycle pulses are used. Comparisons
between these methods show that both the Coulomb force and initial lateral
momentum, which have effects on the $n$-distribution and $l$-distribution of
the population of excited states, are important in the generation of Rydberg
states.
