{"paper":{"title":"Transmutations, L-bases and complete families of solutions of the stationary Schr\\\"odinger equation in the plane","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AP","math.CV","math.MP"],"primary_cat":"math.CA","authors_text":"Hugo M. Campos, Sergii M. Torba, Vladislav V. Kravchenko","submitted_at":"2011-09-27T15:26:00Z","abstract_excerpt":"An L-basis associated to a linear second-order ordinary differential operator L is an infinite sequence of functions {\\phi_k}_{k=0}^{\\infty} such that L\\phi_k=0 for k=0,1, L\\phi_k=k(k-1)\\phi_{k-2}, for k=2,3,... and all \\phi_k satisfy certain prescribed initial conditions. We study the transmutation operators related to L in terms of the transformation of powers of the independent variable {(x-x_{0})^k}_{k=0}^{\\infty} to the elements of the L-basis and establish a precise form of the transmutation operator realizing this transformation. We use this transmutation operator to establish a complet"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.5933","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"}