Quantum superintegrable system with a novel chain structure of quadratic algebras

TL;DR

This paper uncovers a new chain structure of quadratic algebras in an n-dimensional superintegrable Kepler-Coulomb system with non-central terms, leading to an algebraic derivation of its energy spectrum.

Contribution

It introduces a novel chain structure of quadratic algebras in a superintegrable system and constructs its finite-dimensional representations for spectrum analysis.

Findings

Identification of a new chain structure of quadratic algebras

Realization of sub-algebras via deformed oscillators

Algebraic derivation of the energy spectrum

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.