2015/11/10 by Md Fazlul Hoque, Ian Marquette, Yao-Zhong Zhang · 14 citations
Mathematics · Physics and Astronomy · #Casimir effect #Coupling (piping) #Coupling constant #Degenerate energy levels #Lie algebra #Motion (physics) #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Order (exchange) #Quantum Mechanics and Non-Hermitian Physics #Rank (graph theory) #Simple (philosophy) #Unitary state #math-ph #math.MP
paper · pdf · doi:10.1088/1751-8113/49/12/125201
published in Journal of Physics A Mathematical and Theoretical 49(12), 125201 (Institute of Physics) · 19 pages
arxiv created 2015/11/10 · openalex publication_date 2016/02/09 · arxiv updated 2016/02/15 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
By applying the recurrence approach and coupling constant metamorphosis, we construct higher order integrals of motion for the Stackel equivalents of the N -dimensional superintegrable Kepler–Coulomb model with non-central terms and the double singular oscillators of type ( ). We show how the integrals of motion generate higher rank cubic algebra with structure constants involving Casimir operators of the Lie algebras L 1 and L 2 . The realizations of the cubic algebras in terms of deformed oscillators enable us to construct finite dimensional unitary representations and derive the degenerate energy spectra of the corresponding superintegrable systems.