{"paper":{"title":"On Domains of PT Symmetric Operators Related to -y''(x) + (-1)^n x^{2n}y(x)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Carsten Trunk, Tomas Ya. Azizov","submitted_at":"2009-11-06T15:57:47Z","abstract_excerpt":"In the recent years a generalization of Hermiticity was investigated using a complex deformation H=p^2 +x^2(ix)^\\epsilon of the harmonic oscillator Hamiltonian, where \\epsilon is a real parameter. These complex Hamiltonians, possessing PT symmetry (the product of parity and time reversal), can have real spectrum. We will consider the most simple case: \\epsilon even. In this paper we describe all self-adjoint (Hermitian) and at the same time PT symmetric operators associated to H=p^2 +x^2(ix)^\\epsilon. Surprisingly it turns out that there are a large class of self-adjoint operators associated t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.1284","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"}