{"paper":{"title":"The quantum free particle on spherical and hyperbolic spaces: A curvature dependent approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"Jos\\'e F. Cari\\~nena, Manuel F. Ra\\~nada, Mariano Santander","submitted_at":"2012-01-26T17:56:38Z","abstract_excerpt":"The quantum free particle on the sphere $S_\\kappa^2$ ($\\kappa>0$) and on the hyperbolic plane $H_\\kappa^2$ ($\\kappa<0$) is studied using a formalism that considers the curvature $\\k$ as a parameter. The first part is mainly concerned with the analysis of some geometric formalisms appropriate for the description of the dynamics on the spaces ($S_\\kappa^2$, $\\IR^2$, $H_\\kappa^2$) and with the the transition from the classical $\\kappa$-dependent system to the quantum one using the quantization of the Noether momenta. The Schr\\\"odinger separability and the quantum superintegrability are also discu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.5589","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}