Liao, Yidong; Marquette, Ian; Zhang, Yao-Zhong Quantum superintegrable system with a novel chain structure of quadratic algebras. (English) Zbl 1395.81110 J. Phys. A, Math. Theor. 51, No. 25, Article ID 255201, 13 p. (2018). Summary: 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. Cited in 1 ReviewCited in 10 Documents MSC: 81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics 81R12 Groups and algebras in quantum theory and relations with integrable systems 81R15 Operator algebra methods applied to problems in quantum theory 35P05 General topics in linear spectral theory for PDEs 81R05 Finite-dimensional groups and algebras motivated by physics and their representations 35B06 Symmetries, invariants, etc. in context of PDEs Keywords:superintegrable systems; quadratic algebras; Schrödinger equation PDFBibTeX XMLCite \textit{Y. Liao} et al., J. Phys. A, Math. Theor. 51, No. 25, Article ID 255201, 13 p. (2018; Zbl 1395.81110) Full Text: DOI arXiv References: [1] Miller W Jr, Post S and Winternitz P 2013 Classical and quantum superintegrability with applications J. Phys. A: Math. 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