Classical Trajectories for two Ring-Shaped Potentials

Details Classical Trajectories for two Ring-Shaped Potentials Classical Trajectories for two Ring-Shaped Potentials

1998-10-03

arxiv.org/abs/quant-ph/9810006v1

Int.J.Quant.Chem. 43 (1992) 625-645

Physics

Quantum Physics

28 pages, Tex file

Scientific paper

This paper deals with the classical trajectories for two super-integrable systems: a system known in quantum chemistry as the Hartmann system and a system of potential use in quantum chemistry and nuclear physics. Both systems correspond to ring-shaped potentials. They admit two maximally super-integrable systems as limiting cases, viz, the isotropic harmonic oscillator system and the Coulomb-Kepler system in three dimensions. The planarity of the trajectories is studied in a systematic way. In general, the trajectories are quasi-periodic rather than periodic. A constraint condition allows to pass from quasi-periodic motions to periodic ones. When written in a quantum mechanical context, this constraint condition leads to new accidental degeneracies for the two systems studied.

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