{"paper":{"title":"Position-momentum uncertainty products","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Indresh Yadav, Zafar Ahmed","submitted_at":"2014-03-12T06:26:48Z","abstract_excerpt":"We point out two interesting features of position-momentum uncertainty product: $U=\\Delta x \\Delta p$. We show that two special (non-differentiable) eigenstates of the Schr{\\\"o}dinger operator with the Dirac Delta potential $[V(x)=-V_0 \\delta(x)],V_0>0$, also satisfy the Heisenberg's uncertainty principle by yielding $U> \\frac{\\hbar}{2}$. One of these eigenstates is a zero-energy and zero-curvature bound state."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.2824","kind":"arxiv","version":2},"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"}