In this paper we have examined the ionization of the ground state hydrogen atom in a spherical box with laser pulses of specific shapes. These shapes are predicted assuming correspondence under some conditions with the alternating kicking field. Unusually kicked dynamics is suggested. It is shown that such kicked dynamics leads to generalized Rabi oscillations with the positive energy states included and participation of the excited states. The correspondence with the real pulse is established emphasizing such unusually kicked dynamics. The approach is verified on the one-dimensional (1D) hydrogen atom and calculation of the known results for ionization probability.