Nonadiabatic Geometrical Phase during Cyclic Evolution of a Gaussian Wave Packet

Y. C. Ge; M. S. Child

doi:10.1103/PhysRevLett.78.2507

Nonadiabatic Geometrical Phase during Cyclic Evolution of a Gaussian Wave Packet

Y. C. Ge and M. S. Child

Phys. Rev. Lett. 78, 2507 – Published 31 March 1997

Abstract

The Gaussian wave packet solution to the Schrödinger 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 $ħ$ , 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.