2025/11/12 by Herranz, Francisco J., Blasco, Alfonso, Campoamor-Stursberg, Rutwig +3
#Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Physics (quant-ph)
paper · doi:10.48550/arxiv.2511.09541
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.