Generalized classical and quantum Zernike Hamiltonians
Mathematical Physics
2025-12-12 v1 math.MP
Exactly Solvable and Integrable Systems
Quantum Physics
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.
Cite
@article{arxiv.2511.09541,
title = {Generalized classical and quantum Zernike Hamiltonians},
author = {Francisco J. Herranz and Alfonso Blasco and Rutwig Campoamor-Stursberg and Ivan Gutierrez-Sagredo and Danilo Latini and Ian Marquette},
journal= {arXiv preprint arXiv:2511.09541},
year = {2025}
}
Comments
7 pages. Based on the contribution presented at "The XIII International Symposium on Quantum Theory and Symmetries (QTS-13)", 28 July - 1 August, 2025, Yerevan State University, Yerevan, Armenia}