The classical Darboux III oscillator: factorization, Spectrum Generating Algebra and solution to the equations of motion

In a recent paper the so-called Spectrum Generating Algebra (SGA) technique has been applied to the N-dimensional Taub-NUT system, a maximally superintegrable Hamiltonian system which can be interpreted as a one-parameter deformation of the Kepler-Coulomb system. Such a Hamiltonian is associated to...

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Bibliographic Details
Published in:Journal of physics. Conference series 2016-01, Vol.670 (1), p.12031
Main Authors: Latini, D, Ragnisco, O, Ballesteros, A, Enciso, A, Herranz, F J, Riglioni, D
Format: Article
Language:English
Subjects:
Algebra
Curvature
Deformation
Equations of motion
Euclidean geometry
Euclidean space
Hamiltonian functions
Harmonic oscillators
Mathematical analysis
Physics
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Summary:In a recent paper the so-called Spectrum Generating Algebra (SGA) technique has been applied to the N-dimensional Taub-NUT system, a maximally superintegrable Hamiltonian system which can be interpreted as a one-parameter deformation of the Kepler-Coulomb system. Such a Hamiltonian is associated to a specific Bertrand space of non-constant curvature. The SGA procedure unveils the symmetry algebra underlying the Hamiltonian system and, moreover, enables one to solve the equations of motion. Here we will follow the same path to tackle the Darboux III system, another maximally superintegrable system, which can indeed be viewed as a natural deformation of the isotropic harmonic oscillator where the flat Euclidean space is again replaced by another space of non-constant curvature.
ISSN:1742-6588
1742-6596
DOI:10.1088/1742-6596/670/1/012031