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The geometric phases of the cyclic states of a generalized harmonicoscillator with nonadiabatic time-periodic parameters are discussed in theframework of squeezed state. It is shown that the cyclic and quasicyclicsqueezed states correspond to the periodic and quasiperiodic solutions of aneffective Hamiltonian defined on an extended phase space, respectively. Thegeometric phase of the cyclic squeezed state is found to be a phase-space areaswept out by a periodic orbit. Furthermore, a class of cyclic states areexpressed as a superposition of an infinte number of squeezed states. Theirgeometric phases are found to be independent of $\hbar$, and equal to$-(n+1/2)$ times the classical nonadiabatic Hannay angle.Comment: 16 Revtex pages, no figure. Submitted to PR

Nonadiabatic geometric phase for the cyclic evolution of a time-dependent Hamiltonian system