2007/02/24 by José F. Cariñena, Manuel F. Rañada, Mariano Santander
Mathematics · Physics and Astronomy · #Classical mechanics #Constant (computer programming) #Constant curvature #Curvature #Geometry #Harmonic oscillator #Integrable system #Mathematical analysis #Mathematical physics #Mathematics #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Physics #Pure mathematics #Quantization (signal processing) #Quantum #Quantum Mechanics and Non-Hermitian Physics #Quantum mechanics #Separable space #math-ph #math.MP #nlin.SI
paper · pdf · doi:10.3842/sigma.2007.030
published as SIGMA 3 (2007), 030, 23 pages · This is a contribution to the Proc. of workshop on Geometric Aspects of Integrable Systems (July 17-19, 2006; Coimbra, Portugal), published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/
arxiv created 2007/02/24 · openalex publication_date 2007/02/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Two super-integrable and super-separable classical systems which can be considered as deformations of the harmonic oscillator and the Smorodinsky-Winternitz in two dimensions are studied and identified with motions in spaces of constant curvature, the deformation parameter being related with the curvature. In this sense these systems are to be considered as a harmonic oscillator and a Smorodinsky-Winternitz system in such bi-dimensional spaces of constant curvature. The quantization of the first system will be carried out and it is shown that it is super-solvable in the sense that the Schrdinger equation reduces, in three different coordinate systems, to two separate equations involving only one degree of freedom.