{"paper":{"title":"Calculation of the propagator of Schr\\\"odinger's equation on $(0,\\infty)$ with the potential $kx^{-2} + \\omega^2x^2$ by Lie symmetry group method","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"F. G\\\"ung\\\"or","submitted_at":"2018-08-22T09:59:29Z","abstract_excerpt":"The propagators (fundamental solutions) of the heat and Schr\\\"odinger's equations on the half-line with a combined harmonic oscillator and inverse-square potential calculated in the recent paper [{\\em J. Math. Phys.} {\\bf 59}, 051507 (2018)] using Laplace's method are demonstrated to be obtainable alternatively within the framework of symmetry group methods discussed in a series of two papers in the same journal."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.07298","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"}