Nonadiabatic Geometrical Phase during Cyclic Evolution of a Gaussian Wave Packet

Abstract

The Gaussian wave packet solution to the Schr{umlt o}dinger equation is studied for time-dependent Hamiltonians. The geometrical phase is obtained for a cyclic wave packet solution of the generalized harmonic oscillator with a nonadiabatic time-periodic Hamiltonian. It is found that the geometrical phase is independent of {h_bar}, and is equal to one-half of the classical nonadiabatic Hannay angle. The Hannay angle is shown to be independent of the classical action and does not involve averaging. {copyright} {ital 1997} {ital The American Physical Society}