Spin-Orbit Pendulum: the Microscopic Stern-Gerlach Effect

The motion of a particle with a spin in spherical harmonic oscillator potential with spin-orbit interaction is studied. We have focus our attention on spatial motion of wave packets, giving a description complementary to motion of spin discussed already in [1]. The particular initial conditions studied here lead to the most transparent formulas and can be treated analytically. A strong analogy with the Stern-Gerlach experiment is suggested. [1] R.Arvieu and P.Rozmej, Phys.Rev.A50 (1994) 4376.Comment: 4 pages, LaTeX (precisely RevTeX), attached 4 complicated Postscript figures , Paper submitted to Phys.Rev.

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

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