{"paper":{"title":"On the complex solution of the Schr\\\"odinger equation with exponential potentials","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Javier Garcia","submitted_at":"2023-09-12T21:10:02Z","abstract_excerpt":"We study the analytical solutions of the Schr\\\"odinger equation with a repulsive exponential potential $\\lambda e^{- r}$, and that with an exponential wall $\\lambda e^r$, both with $\\lambda > 0$. We show that the complex eigenenergies obtained for the latter tend either to those of the former, or to real rational numbers as $\\lambda \\rightarrow \\infty$. In the light of these results, we explain the wrong resonance energies obtained in a previous application of the Riccati-Pad\\'e method to the Schr\\\"odinger equation with a repulsive exponential potential, and further study the convergence prope"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.06605","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2309.06605/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"}