TIME-DEPENDENT PARTIAL-WAVES AND VORTEX RINGS IN THE DYNAMICS OF WAVEPACKETS

We find a new class of time-dependent partial waves which are solution s of the time-dependent Schrodinger equation for three-dimensional har monic oscillator. We also show the decomposition of coherent states of harmonic oscillator into these partial waves. This decomposition appe ars to be particularly convenient for a description of the dynamics of a wavepacket representing a particle with spin when the spin-orbit in teraction is present in the Hamiltonian. An example of an evolution of a localized wavepacket into a torus and backwards, for particular ini tial conditions is analysed in analytical terms and shown with compute r graphics.