Time dependent partial waves and vortex rings in the dynamics of wave packets

Details Time dependent partial waves and vortex rings in the dynamics of wave packets Time dependent partial waves and vortex rings in the dynamics of wave packets

1997-02-21

arxiv.org/abs/quant-ph/9702043v1

J.Phys.A30:5381-5392,1997

Physics

Quantum Physics

10 pages, LaTeX, 6 postscript figures, submitted to J. Phys. A: Math. Gen

Scientific paper

10.1088/0305-4470/30/15/023

We have found a new class of time dependent partial waves which are solutions of time dependent Schr\"odinger equation for three dimensional harmonic oscillator. We also showed the decomposition of coherent states of harmonic oscillator into these partial waves. This decomposition appears perticularly convenient for a description of the dynamics of a wave packet representing a particle with spin when the spin--orbit interaction is present in the hamiltonian. An example of an evolution of a localized wave packet into a torus and backwards, for a particular initial conditions is analysed in analytical terms and shown with a computer graphics.

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