Models of Quadratic Algebras Generated by Superintegrable Systems in 2D

Abstract

In this paper, we consider operator realizations of quadratic algebras generated by second-order superintegrable systems in 2D. At least one such realization is given for each set of Stäckel equivalent systems for both degenerate and nondegenerate systems. In almost all cases, the models can be used to determine the quantization of energy and eigenvalues for integrals associated with separation of variables in the original system.

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Cited by in corpus (23)

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• Combined state-adding and state-deleting approaches to type III multi-step rationally-extended potentials: applications to ladder operators and superintegrability
• Representations of the rank two Racah algebra and orthogonal multivariate polynomials
• Invariant Classification and Limits of Maximally Superintegrable Systems in 3D
• Infinite families of superintegrable systems separable in subgroup coordinates
• A higher rank extension of the Askey-Wilson Algebra
• Polynomial algebras from $su(3)$ and the generic model on the two sphere
• Bôcher Contractions of Conformally Superintegrable Laplace Equations
• Polynomial algebras of superintegrable systems separating in Cartesian coordinates from higher order ladder operators
• $N$-dimensional Smorodinsky-Winternitz model and related higher rank quadratic algebra $\mathcal{S}\mathcal{W}(N)$
• Bôcher and Abstract Contractions of 2nd Order Quadratic Algebras
• Superintegrable systems, polynomial algebra structures and exact derivations of spectra
• Stäckel Equivalence of Non-Degenerate Superintegrable Systems, and Invariant Quadrics
• Superintegrability and Deformed Oscillator Realizations of Quantum TTW Hamiltonians on Constant-Curvature Manifolds and with Reflections in a Plane
• Polynomial algebras from commutants: Classical and Quantum aspects of ${\mathcal{A}}_3$
• Bocher contractions of conformally superintegrable Laplace equations: Detailed computations
• Construction of polynomial algebras from intermediate Casimir invariants of Lie algebras
• Algebraic structures and Hamiltonians from the equivalence classes of 2D conformal algebras
• Quartic Poisson algebras and quartic associative algebras and realizations as deformed oscillator algebras
• Generalized quadratic commutator algebras of PBW-type
• Tremblay-Turbiner-Winternitz (TTW) system at integer index $k$: polynomial algebras of integrals
• Non-Hermitian superintegrable systems
• Factorized $A_2$-Leonard pair