{"paper":{"title":"A brief discussion on the possible bound states for a class of singular potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Antonio S. de Castro, Douglas R.M. Pimentel","submitted_at":"2013-07-31T20:33:11Z","abstract_excerpt":"The one-dimensional Schr\\\"{o}dinger equation for a class of potentials $V(|x|)$ which vanish at infinity and present dominant singularity at the origin in the form $\\alpha /|x|^{\\beta}$ ($0<\\beta \\leq 2$) is investigated. The Hermiticity of the operators related to observable physical quantities is used to determinate the proper boundary conditions. Double degeneracy and exclusion of symmetric solutions, consonant the value of $\\beta $, are discussed. Explicit solutions for the hydrogen atom and the Kratzer potential are presented."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.0030","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"}