{"paper":{"title":"Isospectral Hermitian counterpart of complex non Hermitian Hamiltonian $p^{2}-gx^{4}+a/x^{2}$","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Asiri Nanayakkara, Thilagarajah Mathanaranjan","submitted_at":"2014-07-17T11:14:47Z","abstract_excerpt":"In this paper we show that the non-Hermitian Hamiltonians $H=p^{2}-gx^{4}+a/x^2$ and the conventional Hermitian Hamiltonians $h=p^2+4gx^{4}+bx$ ($a,b\\in \\mathbb{R}$) are isospectral if $a=(b^2-4g\\hbar^2)/16g$ and $a\\geq -\\hbar^2/4$. This new class includes the equivalent non-Hermitian - Hermitian Hamiltonian pair, $p^{2}-gx^{4}$ and $p^{2}+4gx^{4}-2\\hbar \\sqrt{g}x,$ found by Jones and Mateo six years ago as a special case. When $a=\\left(b^{2}-4g\\hbar ^{2}\\right) /16g$ and $a<-\\hbar^2/4,$ although $h$ and $H$ are still isospectral, $b$ is complex and $h$ is no longer the Hermitian counterpart o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.4633","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"}