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

23rd International Conference on Integrable Systems and Quantum Symmetries

Latini, D.^3 ; Ragnisco, O.^3 ; Ballesteros, A.^1 ; Enciso, A.^2 ; Herranz, F.J.^1 ; Riglioni, D.^3

Departamento de Flsíca, Universidad de Burgos, Burgos

E-09001, Spain^1

Instituto de Ciencias Matemáticas, CSIC, Nicolás Cabrera 13-15, Madrid

E-28049, Spain^2

Dipartimento di Matematica e Fisica, Universitá di Roma Tre, Istituto Nazionale di Fisica Nucleare Sezione di Roma Tre, Via Vasca Navale 84, Roma

I-00146, Italy^3

关键词: Bertrand;    Constant curvature;    Coulomb systems;    Euclidean spaces;    Hamiltonian systems;    Harmonic oscillators;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/670/1/012031/pdf
DOI  :  10.1088/1742-6596/670/1/012031

来源: IOP

【 摘 要 】

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.