Partial revivals of wave packets: An action-angle phase-space description

Partial revivals of wave packets are investigated by means of the action-angle Wigner function, which is formulated in terms of action quantum numbers and angle variables. In the eigenbasis of the Hamiltonian, the phase shifts of the expansion coefficients of the wave packet are approximated by a quadratic function of action quantum numbers. Under this approximation, the evolution of the action-angle Wigner function of the wave packet, similarly to the classical Liouville density, can be viewed as a result of each phase-space point moving along a classical orbit. The partial and full revivals of wave packets are direct consequences of two facts: (i) The action-angle Wigner function is distributed only on discrete tori of the phase space and (ii) phase-space points of nearby tori move against each other with a constant speed.