{"paper":{"title":"Curvature-dependent formalism, Schr\\\"odinger equation and energy levels for the harmonic oscillator on three-dimensional spherical and hyperbolic spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"Jos\\'e F. Cari\\~nena, Manuel F. Ra\\~nada, Mariano Santander","submitted_at":"2012-10-18T08:49:09Z","abstract_excerpt":"A nonlinear model representing the quantum harmonic oscillator on the three-dimensional spherical and hyperbolic spaces, $S_\\k^3$ ($\\kappa>0$) and $H_k^3$ ($\\kappa<0$), is studied. The curvature $\\k$ is considered as a parameter and then the radial Schr\\\"odinger equation becomes a $\\k$-dependent Gauss hypergeometric equation that can be considered as a $\\k$-deformation of the confluent hypergeometric equation that appears in the Euclidean case.\n  The energy spectrum and the wavefunctions are exactly obtained in both the three-dimensional sphere $S_\\k^3$ ($\\kappa>0$) and the hyperbolic space $H"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.5055","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"}