Quantum particle trajectories and geometric phase

Particle trajectories are defined as integrable dxμdpμ=0 paths in projective space. Quantum states evolving on such trajectories, open or closed, do not delocalize in (x, p) projection, the phase associated with the trajectories related to the geometric (Berry) phase and the classical mechanics action. Properties at high energies of the states evolving on particle trajectories are discussed.