{"paper":{"title":"A nodal domain theorem for integrable billiards in two dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["quant-ph"],"primary_cat":"nlin.SI","authors_text":"Rhine Samajdar, Sudhir R. Jain","submitted_at":"2014-04-21T18:50:34Z","abstract_excerpt":"Eigenfunctions of integrable planar billiards are studied - in particular, the number of nodal domains, $\\nu$, of the eigenfunctions are considered. The billiards for which the time-independent Schr\\\"odinger equation (Helmholtz equation) is separable admit trivial expressions for the number of domains. Here, we discover that for all separable and non-separable integrable billiards, $\\nu $ satisfies certain difference equations. This has been possible because the eigenfunctions can be classified in families labelled by the same value of $m\\mod kn$, given a particular $k$, for a set of quantum n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.5269","kind":"arxiv","version":3},"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"}