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Generalized classical and quantum Zernike Hamiltonians
Francisco J. Herranz, Alfonso Blasco, Rutwig Campoamor-Stursberg, Ivan Gutierrez-Sagredo, Danilo Latini, Ian Marquette·November 12, 2025·DOI: 10.55318/bgjp.2025.52.s1.139
Mathematical Physicsnlin.SIQuantum Physics
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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.