dorsal/arxiv
View SchemaClassical Trajectories for two Ring-Shaped Potentials
| Authors | M. Kibler, G. -H. Lamot, P. Winternitz |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9810006 |
| URL | https://arxiv.org/abs/quant-ph/9810006 |
| Journal | Int.J.Quant.Chem. 43 (1992) 625-645 |
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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"abstract": "This paper deals with the classical trajectories for two super-integrable\nsystems: a system known in quantum chemistry as the Hartmann system and a\nsystem of potential use in quantum chemistry and nuclear physics. Both systems\ncorrespond to ring-shaped potentials. They admit two maximally super-integrable\nsystems as limiting cases, viz, the isotropic harmonic oscillator system and\nthe Coulomb-Kepler system in three dimensions. The planarity of the\ntrajectories is studied in a systematic way. In general, the trajectories are\nquasi-periodic rather than periodic. A constraint condition allows to pass from\nquasi-periodic motions to periodic ones. When written in a quantum mechanical\ncontext, this constraint condition leads to new accidental degeneracies for the\ntwo systems studied.",
"arxiv_id": "quant-ph/9810006",
"authors": [
"M. Kibler",
"G. -H. Lamot",
"P. Winternitz"
],
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"quant-ph",
"physics.chem-ph",
"physics.class-ph"
],
"journal_ref": "Int.J.Quant.Chem. 43 (1992) 625-645",
"title": "Classical Trajectories for two Ring-Shaped Potentials",
"url": "https://arxiv.org/abs/quant-ph/9810006"
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