{"paper":{"title":"The exactly solvable two-dimensional stationary Schr\\\"odinger operators obtaining by the nonlocal Darboux transformation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"Andrey Kudryavtsev","submitted_at":"2012-11-24T17:35:12Z","abstract_excerpt":"The Fokker-Planck equation associated with the two - dimensional stationary Schr\\\"odinger equation has the conservation low form that yields a pair of potential equations. The special form of Darboux transformation of the potential equations system is considered. As the potential variable is a nonlocal variable for the Schr\\\"odinger equation that provides the nonlocal Darboux transformation for the Schr\\\"odinger equation. This nonlocal transformation is applied for obtaining of the exactly solvable two - dimensional stationary Schr\\\"odinger equations. The examples of exactly solvable two - dim"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.5685","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"}