{"paper":{"title":"Singularity in Potential, Perturbation and Variational Methods","license":"","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"Peng-Nian Shen, Xue-Qian Li, Yi-Bing Ding","submitted_at":"1999-02-12T08:32:39Z","abstract_excerpt":"In this work, we carefully study the energy eigen-values and splitting of heavy quarkonia as there exist $1/r^3$ and $\\delta^3(\\vec r)$ singular terms in the potential which make a direct numerical solution of the Schr\\\"{o}dinger equation impossible. We compare the results obtained in terms of perturbation and variational methods with various treatments."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-ph/9902330","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"}