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Classical trajectories for two ring‐shaped potentials
Author(s) -
Kibler Maurice,
Lamot GeorgesHenri,
Winternitz Pavel
Publication year - 1992
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560430503
Subject(s) - harmonic oscillator , ring (chemistry) , quantum , context (archaeology) , isotropy , physics , classical mechanics , quantum system , constraint (computer aided design) , periodic system , anharmonicity , planarity testing , quantum mechanics , mathematical physics , mathematics , mathematical analysis , chemistry , geometry , crystallography , paleontology , organic chemistry , biology
The present paper deals with the classical trajectories for two superintegrable 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 superintegrable 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. © 1992 John Wiley & Sons, Inc.