The spherical version of the two-dimensional central harmonic oscillator, as well as the spherical Kepler (Schrödinger) potential, are superintegrable systems with quadratic constants of motion. They belong to two different spherical "Smorodinski-Winternitz" families of superintegrable potentials. A new superintegrable oscillator have been recently found in S². It represents the spherical version of the nonisotropic 2:1 oscillator and it also belongs to a spherical family of quadratic superintegrable potentials. In the first part of the article, several properties related to the integrability and superintegrability of these spherical families of potentials are studied. The second part is devoted to the analysis of the properties of the spherical (isotropic and nonisotropic) harmonic oscillators.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc59-0-13,
author = {Manuel F. Ra\~nada and Teresa Sanz-Gil and Mariano Santander},
title = {Superintegrable Potentials and superposition of Higgs Oscillators on the Sphere S$^2$},
journal = {Banach Center Publications},
volume = {60},
year = {2003},
pages = {243-255},
zbl = {1022.37039},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc59-0-13}
}
Manuel F. Rañada; Teresa Sanz-Gil; Mariano Santander. Superintegrable Potentials and superposition of Higgs Oscillators on the Sphere S². Banach Center Publications, Tome 60 (2003) pp. 243-255. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc59-0-13/