{"paper":{"title":"A Schr\\\"odinger potential involving $x^\\frac{2}{3}$ and centrifugal-barrier terms conditionally integrable in terms of the confluent hypergeometric functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"A.M. Ishkhanyan, T.A. Ishkhanyan, V.A. Manukyan","submitted_at":"2019-06-23T20:09:28Z","abstract_excerpt":"The solution of the one-dimensional Schr\\\"odinger equation for a potential involving an attractive $x^\\frac{2}{3}$ and a repulsive centrifugal-barrier $\\sim x^{-2}$ terms is presented in terms of the non-integer-order Hermite functions. The potential belongs to one of the five bi-confluent Heun families. This is a conditionally integrable potential in that the strength of the centrifugal-barrier term is fixed. The general solution of the problem is composed using fundamental solutions each of which presents an irreducible linear combination of two Hermite functions of a scaled and shifted argu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.10123","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"}