Quantum superintegrable system with a novel chain structure of quadratic algebras

Abstract

We analyse the $n$-dimensional superintegrable Kepler-Coulomb system with non-central terms. We find a novel underlying chain structure of quadratic algebras formed by the integrals of motion. We identify the elements for each sub-structure and obtain the algebra relations satisfied by them and the corresponding Casimir operators. These quadratic sub-algebras are realized in terms of a chain of deformed oscillators with factorized structure functions. We construct the finite-dimensional unitary representations of the deformed oscillators, and give an algebraic derivation of the energy spectrum of the superintegrable system.

LaTex 12 pages, 4 figures. Version to appear in J. Phys. A: Math. Theor

References in corpus (2)

• A superintegrable model with reflections on $S^{n-1}$ and the higher rank Bannai-Ito algebra
• Hidden supersymmetry and quadratic deformations of the space-time conformal superalgebra

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