On periodically kicked quantum systems

The time evolution of a multi-dimensional system which is kicked periodically with a potential is obtained. The most interesting aspects of the investigation are (i) if the operator corresponding to the potential has invariant subspaces (a characteristic property of multidimensional systems), the states belonging to these subspace in its evolution are confined to these invariant subspaces respectively and there cannot be any mixing of states between these subspaces. Further, (ii) it leads to the existence of quasi-stationary states (determined again by the potential) which evolves independent of other similar quasi-stationary states. The method followed in the paper is the direct integration of the Schrödinger equation and then to construct the wave function from the initial wave function.