2011/04/02 by C. Quesne, Christiane Quesne
Mathematics · Physics and Astronomy · #Algebra over a field #Algebraic number #Dynamical systems theory #Geometry #Hamiltonian (control theory) #Hamiltonian system #Harmonic oscillator #Homogeneous space #Mathematical analysis #Mathematical physics #Mathematics #Nonlinear Photonic Systems #Physics #Pure mathematics #Quantum #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Quantum mechanics #Wave function #math-ph #math.MP #quant-ph
paper · pdf · doi:10.3842/sigma.2011.035
published as SIGMA 7:035,2011
arxiv created 2011/04/02 · openalex publication_date 2011/04/02 · arxiv updated 2011/11/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The D-dimensional Smorodinsky-Winternitz system, proposed some years ago by Evans, is re-examined from an algebraic viewpoint. It is shown to possess a potential algebra, as well as a dynamical potential one, in addition to its known symmetry and dynamical algebras. The first two are obtained in hyperspherical coordinates by introducing D auxiliary continuous variables and by reducing a 2D-dimensional harmonic oscillator Hamiltonian. The su(2D) symmetry and w(2D) s sp(4D, R) dynamical algebras of this Hamiltonian are then transformed into the searched for potential and dynamical potential algebras of the Smorodinsky-Winternitz system. The action of generators on wavefunctions is given in explicit form for D = 2.