We present explicit expressions for the Floquet states of a periodically kicked particle in coordinate and momentum representations. These states have been used to evaluate the energy of the particle after an arbitrary number of kicks.

The quantal behaviour of wave packet periodically kicked by a quadratic potential has been investigated using Floquet theory. The wave function of the particle afterN kicks has been determined. This wave function has been utilized to obtain the packet width, energy and loss of memory as a function of the number of kicks. It has also been shown that the free particle wave packet quasienergy spectrum makes a transition from discrete to absolutely continuous atɛ T=2. The behaviour forɛT>2 is quantum mechanically irregular.

The problem of a free electron periodically kicked by a magnetic field has been solved. The system shows a transition from quantum recurrence to instability at ωT=2 where ω is the Larmor frequency andT is the period of the kick. The existence of recurrent behaviour amounts to the confinement of the electron by magnetic kicking. Since the theory holds for all types of charged particles, it has many practical applications.