{"paper":{"title":"On the eigenproblems of PT-symmetric oscillators","license":"","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"K. C. Shin","submitted_at":"2000-07-05T07:42:34Z","abstract_excerpt":"We consider the non-Hermitian Hamiltonian H= -\\frac{d^2}{dx^2}+P(x^2)-(ix)^{2n+1} on the real line, where P(x) is a polynomial of degree at most n \\geq 1 with all nonnegative real coefficients (possibly P\\equiv 0). It is proved that the eigenvalues \\lambda must be in the sector | arg \\lambda | \\leq \\frac{\\pi}{2n+3}. Also for the case H=-\\frac{d^2}{dx^2}-(ix)^3, we establish a zero-free region of the eigenfunction u and its derivative u^\\prime and we find some other interesting properties of eigenfunctions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0007006","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math-ph/0007006/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}