{"paper":{"title":"Unusual isospectral factorizations of shape invariant Hamiltonians with Scarf II potential","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"\\c{S}eng\\\"ul Kuru, Lorena Acevedo, Yi\\u{g}it Can Acar","submitted_at":"2023-09-12T08:28:34Z","abstract_excerpt":"In this paper, we search the factorizations of the shape invariant Hamiltonians with Scarf II potential. We find two classes; one of them is the standard real factorization which leads us to a real hierarchy of potentials and their energy levels; the other one is complex and it leads us naturally to a hierarchy of complex Hamiltonians. We will show some properties of these complex Hamiltonians: they are not parity-time (or PT) symmetric, but their spectrum is real and isospectral to the Scarf II real Hamiltonian hierarchy. The algebras for real and complex shift operators (also called potentia"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.06044","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2309.06044/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}