{"paper":{"title":"A Quantum Exactly Solvable Nonlinear Oscillator with quasi-Harmonic Behaviour","license":"","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":"2006-04-05T08:30:31Z","abstract_excerpt":"The quantum version of a non-linear oscillator, previouly analyzed at the classical level, is studied. This is a problem of quantization of a system with position-dependent mass of the form $m={(1+\\lambda x^2)}^{-1}$ and with a $\\la$-dependent nonpolynomial rational potential. This $\\la$-dependent system can be considered as a deformation of the harmonic oscillator in the sense that for $\\la\\to 0$ all the characteristics of the linear oscillator are recovered. Firstly, the $\\la$-dependent Schr\\\"odinger equation is exactly solved as a Sturm-Liouville problem and the $\\la$-dependent eigenenergie"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0604008","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"}