Superintegrable Potentials and superposition of Higgs Oscillators on the Sphere S²

Manuel F. Rañada, Teresa Sanz-Gil, and Mariano Santander. "Superintegrable Potentials and superposition of Higgs Oscillators on the Sphere S²." Banach Center Publications 59.1 (2003): 243-255. <http://eudml.org/doc/282418>.

@article{ManuelF2003,
abstract = {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.},
author = {Manuel F. Rañada, Teresa Sanz-Gil, Mariano Santander},
journal = {Banach Center Publications},
keywords = {integrability; separability; superintegrable systems; spaces of constant curvature; quadratic constants of motion},
language = {eng},
number = {1},
pages = {243-255},
title = {Superintegrable Potentials and superposition of Higgs Oscillators on the Sphere S²},
url = {http://eudml.org/doc/282418},
volume = {59},
year = {2003},
}

TY - JOUR
AU - Manuel F. Rañada
AU - Teresa Sanz-Gil
AU - Mariano Santander
TI - Superintegrable Potentials and superposition of Higgs Oscillators on the Sphere S²
JO - Banach Center Publications
PY - 2003
VL - 59
IS - 1
SP - 243
EP - 255
AB - 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.
LA - eng
KW - integrability; separability; superintegrable systems; spaces of constant curvature; quadratic constants of motion
UR - http://eudml.org/doc/282418
ER -