{"paper":{"title":"Nodal theorems for the Dirac equation in d >= 1 dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"Petr Zorin, Richard L. Hall","submitted_at":"2013-09-06T19:32:52Z","abstract_excerpt":"A single particle obeys the Dirac equation in $d \\ge 1$ spatial dimensions and is bound by an attractive central monotone potential that vanishes at infinity. In one dimension, the potential is even, and monotone for $x\\ge 0.$ The asymptotic behavior of the wave functions near the origin and at infinity are discussed. Nodal theorems are proven for the cases $d=1$ and $d > 1$, which specify the relationship between the numbers of nodes $n_1$ and $n_2$ in the upper and lower components of the Dirac spinor. For $d=1$, $n_2 = n_1 + 1,$ whereas for $d >1,$ $n_2 = n_1 +1$ if $k_d > 0,$ and $n_2 = n_"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.1749","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"}