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arXiv · 1801.05634

Quantum superintegrable system with a novel chain structure of quadratic algebras

Yidong Liao·Ian Marquette·Yao-Zhong Zhang
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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.

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Yidong Liao, Ian Marquette, Yao-Zhong Zhang. 2018-01-17. Quantum superintegrable system with a novel chain structure of quadratic algebras. https://doi.org/10.1088/1751-8121%2Faac111

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