{"paper":{"title":"Quantum Particle Dynamics in a Highly Singular 1D-Potential $U(x) = -\\alpha \\delta(x) + \\beta \\delta'(x)$ Superposed on a Well-Behaved One","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Norman J. Morgenstern Horing","submitted_at":"2014-11-25T02:01:56Z","abstract_excerpt":"We examine the one-dimensional quantum dynamics of a Schroedinger particle in a potential represented by a generalized function of the form $U(x) = -\\alpha \\delta (x) + \\beta d(\\delta (x))/dx$ superposed on a well behaved potential $V(x)$. In this, we construct the full, exact Green's function for such a 1D system analytically in closed form, taking account of a spatially variable mass $m(x)$. Our result shows that there can be no electron transmission through the $\\beta \\delta '(x)$- potential, regardless of the presence of the $V(x)$- potential and $\\alpha \\delta (x)$, (with $\\alpha \\ne 0$)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.6703","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"}