Dynamical symmetry, integrability of quantum systems, and general character of quantum regular motion - art. no. 042104

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.