Superintegrable Potentials and superposition of Higgs Oscillators on the Sphere S²

• Autorzy: Manuel F. Rañada , Teresa Sanz-Gil , Mariano Santander
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 70H06: Completely integrable systems and methods of integration
• 37J35: Completely integrable systems, topological structure of phase space, integration methods
• 37J15: Symmetries, invariants, invariant manifolds, momentum maps, reduction

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2003
• Tom: 59
• Numer: 1
• Strony: 243-255

Daty

wydano

2003

Twórcy

autor

Manuel F. Rañada

• Departamento de Física Teórica, Facultad de Ciencias, Universidad de Zaragoza, 50009 Zaragoza, Spain

autor

Teresa Sanz-Gil

• Departamento de Física Teórica, Facultad de Ciencias, Universidad de Valladolid, 47011 Valladolid, Spain

autor

Mariano Santander

• Departamento de Física Teórica, Facultad de Ciencias, Universidad de Valladolid, 47011 Valladolid, Spain

Identyfikatory

DOI

10.4064/bc59-0-13