{"paper":{"title":"Operator based approach to PT-symmetric problems on a wedge-shaped contour","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"Carsten Trunk, Florian Leben","submitted_at":"2019-02-21T13:15:25Z","abstract_excerpt":"We consider a second-order differential equation $$ -y''(z)-(iz)^{N+2}y(z)=\\lambda y(z), \\quad z\\in \\Gamma $$ with an eigenvalue parameter $\\lambda \\in \\mathbb{C}$. In $\\mathcal{PT}$ quantum mechanics $z$ runs through a complex contour $\\Gamma\\subset \\mathbb{C}$, which is in general not the real line nor a real half-line. Via a parametrization we map the problem back to the real line and obtain two differential equations on $[0,\\infty)$ and on $(-\\infty,0].$ They are coupled in zero by boundary conditions and their potentials are not real-valued. The main result is a classification of this pro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.08025","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"}