Quasiclassical states of the Coulomb system and so(4, 2)

Quasiclassical bound states of the quantum mechanical Coulomb system are constructed. They are initially Barut-Girardello coherent states of the natural so(4, 2) dynamical algebra, and evolve in accordance with the Schrodinger equation. The asymptotic behaviour of expectation values and uncertainties of all the so(4, 2) observables is examined in detail for those states having a mean value of n, the principal quantum number, approaching infinity. There is no spreading with respect to these observables over times of the order of tau , the corresponding classical period, but the states do spread over times of the order of tau 7 6/. Periodic but successively weaker resurgences of coherence are found over times of the order of tau 4 3/. It is shown explicitly that the states are quasiperiodic over extremely long times.