Abstract

We study the dynamics of a circular-orbit wave packet¹ and find that it has both classical and quantum features. A circular-orbit wave packet consists of aligned, standard hydrogenic eigenstates of maximum angular momentum (l = in = n − 1), superimposed with a Gaussian weighting function. We calculate the uncertainty products in all three degrees of freedom and find that, as the quantum numbers of the constituent eigenstates increase, the uncertainty products tend toward h/2. The classical aspect of the dynamics displays itself during revivals, when a well-localized wave packet travels along a Kepler orbit, obeying the classical equations of motion. Spreading and revivals (including fractional revivals²) of the wave packet, which are manifestations of its quantum nature, are related to the nonlinearity of the hydrogen atom Hamiltonian. We study fractional revivals of the wavepacket in detail.

© 1990 Optical Society of America