R. Arvieu et al., TIME-DEPENDENT PARTIAL-WAVES AND VORTEX RINGS IN THE DYNAMICS OF WAVEPACKETS, Journal of physics. A, mathematical and general, 30(15), 1997, pp. 5381-5392
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.