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arXiv · 2511.09541

Generalized classical and quantum Zernike Hamiltonians

Francisco J. Herranz·Alfonso Blasco·Rutwig Campoamor-Stursberg·Ivan Gutierrez-Sagredo·Danilo Latini·Ian Marquette
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Abstract

A superintegrable generalization of the classical and quantum Zernike systems is reviewed. The corresponding Hamiltonians are endowed with higher-order integrals and can be interpreted as higher-order superintegrable perturbations of the 2D spherical (Higgs), hyperbolic, and Euclidean harmonic oscillators. As a new result, the complete polynomial Higgs-type symmetry algebra of the generalized classical system is presented. For the generalized quantum system, the symmetry algebra and the spectra are provided for a representative case.

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Francisco J. Herranz, Alfonso Blasco, Rutwig Campoamor-Stursberg, Ivan Gutierrez-Sagredo, Danilo Latini, Ian Marquette. 2025-11-12. Generalized classical and quantum Zernike Hamiltonians. https://doi.org/10.55318/bgjp.2025.52.s1.139

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