Generalized classical and quantum Zernike Hamiltonians
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arXiv
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| Main Authors: | , , , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909955897950208 |
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| author | Herranz, Francisco J. Blasco, Alfonso Campoamor-Stursberg, Rutwig Gutierrez-Sagredo, Ivan Latini, Danilo Marquette, Ian |
| author_facet | Herranz, Francisco J. Blasco, Alfonso Campoamor-Stursberg, Rutwig Gutierrez-Sagredo, Ivan Latini, Danilo Marquette, Ian |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_09541 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Generalized classical and quantum Zernike Hamiltonians Herranz, Francisco J. Blasco, Alfonso Campoamor-Stursberg, Rutwig Gutierrez-Sagredo, Ivan Latini, Danilo Marquette, Ian Mathematical Physics Exactly Solvable and Integrable Systems Quantum Physics 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. |
| title | Generalized classical and quantum Zernike Hamiltonians |
| topic | Mathematical Physics Exactly Solvable and Integrable Systems Quantum Physics |
| url | https://arxiv.org/abs/2511.09541 |