Quadratic algebra structure and spectrum of a new superintegrable system in N-dimension

Abstract

We introduce a new superintegrable Kepler-Coulomb system with non-central terms in $N$-dimensional Euclidean space. We show this system is multiseparable and allows separation of variables in hyperspherical and hyperparabolic coordinates. We present the wave function in terms of special functions. We give a algebraic derivation of spectrum of the superintegrable system. We show how the $so(N+1)$ symmetry algebra of the $N$-dimensional Kepler-Coulomb system is deformed to a quadratic algebra with only 3 generators and structure constants involving a Casimir operator of $so(N-1)$ Lie algebra. We construct the quadratic algebra and the Casimir operator. We show this algebra can be realized in terms of deformed oscillator and obtain the structure function which yields the energy spectrum.

21 pages

References in corpus (3)

• Non-Abelian magnetic monopole in a Bose-Einstein condensate
• Generalized MICZ-Kepler system, duality, polynomial and deformed oscillator algebras
• Algebraic Calculation of the Energy Eigenvalues for the Nondegenerate Three-Dimensional Kepler-Coulomb Potential

Cited by in corpus (6)

• Embedding of the Racah Algebra R($\mathbf{n}$) and Superintegrability
• Racah Algebra $R(n)$ from Coalgebraic Structures and Chains of $R(3)$ Substructures
• $N$-dimensional Smorodinsky-Winternitz model and related higher rank quadratic algebra $\mathcal{S}\mathcal{W}(N)$
• Polynomial algebras of superintegrable systems separating in Cartesian coordinates from higher order ladder operators
• Superintegrability and Deformed Oscillator Realizations of Quantum TTW Hamiltonians on Constant-Curvature Manifolds and with Reflections in a Plane
• Polynomial deformations of $sl(2)$ and unified algebraic framework for solutions of a class of spin models