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Quantum superintegrable system with a novel chain structure of quadratic algebras. (English) Zbl 1395.81110

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.

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
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References:

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