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Recurrence approach and higher rank cubic algebras for theN-dimensional superintegrable systems

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

Abstract

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.

Citations