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Classical Trajectories for two Ring-Shaped Potentials

Abstract : 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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Contributor : Dominique Girod <>
Submitted on : Thursday, November 23, 2006 - 10:27:30 AM
Last modification on : Thursday, June 17, 2021 - 3:18:32 PM

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M. Kibler, G.-H. Lamot, P. Winternitz. Classical Trajectories for two Ring-Shaped Potentials. International Journal of Quantum Chemistry, Wiley, 1998, 43, pp.625-645. ⟨10.1002/qua.560430503⟩. ⟨in2p3-00115760⟩



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