{"paper":{"title":"The quantum free particle on spherical and hyperbolic spaces: A curvature dependent approach II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"Jos\\'e F. Cari\\~nena, Manuel F. Ra\\~nada, Mariano Santander","submitted_at":"2012-11-09T09:01:13Z","abstract_excerpt":"This paper is the second part of a study of the quantum free particle on spherical and hyperbolic spaces by making use of a curvature-dependent formalism. Here we study the analogues, on the three-dimensional spherical and hyperbolic spaces, $S_\\k^3$ ($\\kappa>0$) and $H_\\k^3$ ($\\kappa<0$), to the standard {\\itshape spherical waves} in $E^3$. The curvature $\\k$ is considered as a parameter and for any $\\k$ we show how the radial Schr\\\"odinger equation can be transformed into a $\\k$-dependent Gauss hypergeometric equation that can be considered as a $\\k$-deformation of the (spherical) Bessel equ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.2076","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"}