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arXiv · 1605.06213

Recurrence approach and higher rank polynomial algebras for superintegrable monopole systems

Md Fazlul Hoque·Ian Marquette·Yao-Zhong Zhang
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Abstract

We revisit the MIC-harmonic oscillator in flat space with monopole interaction and derive the polynomial algebra satisfied by the integrals of motion and its energy spectrum using the ad hoc recurrence approach. We introduce a superintegrable monopole system in generalized Taub-NUT space. The Schrödinger equation of this model is solved in spherical coordinates in the framework of Stäckel transformation. It is shown that wave functions of the quantum system can be expressed in terms of the product of Laguerre and Jacobi polynomials. We construct ladder and shift operators based on the corresponding wave functions and obtain the recurrence formulas. By applying these recurrence relations, we construct higher order algebraically independent integrals of motion. We show the integrals form a polynomial algebra. We construct the structure functions of the polynomial algebra and obtain the degenerate energy spectra of the model.

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Md Fazlul Hoque, Ian Marquette, Yao-Zhong Zhang. 2016-05-20. Recurrence approach and higher rank polynomial algebras for superintegrable monopole systems. https://doi.org/10.1063/1.5012859

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