THE AHARONOV-ANANDAN PHASE FOR QUASI-ENERGY TRAJECTORY-COHERENT STATES

Quasi-energy spectral series [epsilon(n)u(($) over cap h), psi(epsilon nu)] which, in the limit ($) over cap h --> 0, correspond to stable m otions of a classical system along closed phase trajectories are built up in terms of a quasi-classical approximation for the Schrodinger eq uation with an arbitrary T-periodic ($) over cap h(-1)-(pseudo)differe ntial Hamilton operator. Using the procedure of splitting the quantum- mechanical phase into dynamic and geometric components, the 'geometric ' contribution of the Aharonov-Anandan phase y(epsilon nu) to the quas i-energy spectrum is calculated. It is shown that the y(epsilon nu) ph ase, in the adiabatic approximation, coincides with the Berry phase th at corresponds to a cyclic evolution of a stable rest-point of a class ical system. Some examples are considered.