Sudden switching in two-state systems

Analytic solutions are developed for two-state systems strongly perturbed by a series of rapidly changing pulses, called 'kicks'. The evolution matrix may be expressed as a time orrdered product of evolution matricies for single kicks. Single, double and triple kicks are explicitly considered, and the onset of time ordering is examined. The effects of different order of kicks on the dynamics of the system is studied and commpared with effects of time ordering in general. To determine the range of validity of this apporach, the effect of using pulses of finite widths for 2s - 2p transitions in atomic hydrogen is examined numerically.