{"paper":{"title":"Generalized Lennard-Jones Potentials, SUSYQM and Differential Galois Theory","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"Erick Tuir\\'an, Manuel F. Acosta-Hum\\'anez, Primitivo B. Acosta-Hum\\'anez","submitted_at":"2018-03-03T21:37:32Z","abstract_excerpt":"In this paper we start with proving that the Schr\\\"odinger equation (SE) with the classical $12-6$ Lennard-Jones (L-J) potential is nonintegrable in the sense of the differential Galois theory (DGT), for any value of energy; i.e., there are no solutions in closed form for such differential equation. We study the $10-6$ potential through DGT and SUSYQM; being it one of the two partner potentials built with a superpotential of the form $w(r)\\propto 1/r^5$. We also find that it is integrable in the sense of DGT for zero energy. A first analysis of the applicability and physical consequences of th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.01247","kind":"arxiv","version":4},"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"}