Go. Xu et al., Dynamical symmetry, integrability of quantum systems, and general character of quantum regular motion - art. no. 042104, PHYS REV A, 6104(4), 2000, pp. 2104
The notion of quantum-classical correspondence is carefully investigated in
order to prepare firm grounds for studying the spatiotemporal evolution of
quantum states in the same spirit as for corresponding classical cases. Th
ree relevant problems, (1) the integrability of dynamical equations of quan
tum systems, (2) the initial minimum uncertainty states one-to-one correspo
ndent to classical phase points, and (3) the effective Planck constants for
systems having analogous dynamical properties but exhibiting different qua
ntum effects, have been successfully resolved. Then the solution rho(gamma)
(t) of the dynamical equation of a quantum integrable system is shown to be
expressed as an analytical functional of the initial minimum uncertainty s
tate rho(gamma)(o) varying smoothly with gamma and t. Such a general charac
ter of the quantum regular motion serves as a reference for the study of qu
antum irregular motion under the action of perturbed Hamiltonian.