{"paper":{"title":"Zero Energy Solutions and Vortices in Schroedinger Equations","license":"","headline":"","cross_cats":["cond-mat.mtrl-sci"],"primary_cat":"cond-mat.mes-hall","authors_text":"Toshiki Shimbori, Tsunehiro Kobayashi","submitted_at":"2001-03-09T06:20:57Z","abstract_excerpt":"All two-dimensional Schr\\\"{o}dinger equations with symmetric potentials \\break $(V_a(\\rho)=-a^2g_a \\rho ^{2(a-1)/2} {with} \\rho=\\sqrt{x^2+y^2} {and} a\\not=0)$ is shown to have zero energy states contained in conjugate spaces of Gel'fand triplets. For the zero energy eigenvalue the equations for all $a$ are reduced to the same equation representing two-dimensional free motions in the constant potential $V_a=-g_a$ in terms of the conformal mappings of $\\zeta_a=z^a$ with $z=x+iy$. Namely, the zero energy eigenstates are described by the plane waves with the fixed wave numbers $k_a=\\sqrt{mg_a}/\\hb"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0103209","kind":"arxiv","version":4},"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"}