{"paper":{"title":"Generalized quantum Zernike Hamiltonians: Polynomial Higgs-type algebras and algebraic derivation of the spectrum","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","nlin.SI"],"primary_cat":"quant-ph","authors_text":"Alfonso Blasco, Danilo Latini, Francisco J. Herranz, Ian Marquette, Rutwig Campoamor-Stursberg","submitted_at":"2025-02-04T17:06:54Z","abstract_excerpt":"We consider the quantum analog of the generalized Zernike systems given by the Hamiltonian: $$\\hat{\\mathcal{H}}_N =\\hat{p}_1^2+\\hat{p}_2^2+\\sum_{k=1}^N \\gamma_k (\\hat{q}_1 \\hat{p}_1+\\hat{q}_2 \\hat{p}_2)^k ,$$ with canonical operators $\\hat{q}_i,\\, \\hat{p}_i$ and arbitrary coefficients $\\gamma_k$. This two-dimensional quantum model, besides the conservation of the angular momentum, exhibits higher-order integrals of motion within the enveloping algebra of the Heisenberg algebra in two dimensions. By constructing suitable combinations of these integrals, we uncover a polynomial Higgs-type symmet"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.02491","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2502.02491/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}