{"paper":{"title":"The spectrum of the cubic oscillator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.SP"],"primary_cat":"math-ph","authors_text":"Andr\\'e Martinez, Vincenzo Grecchi","submitted_at":"2012-01-13T10:45:27Z","abstract_excerpt":"We prove the simplicity and analyticity of the eigenvalues of the cubic oscillator Hamiltonian,$H(\\beta)=-d^2/dx^2+x^2+i\\sqrt{\\beta}x^3$,for $\\beta$ in the cut plane $\\C_c:=\\C\\backslash (-\\infty, 0)$. Moreover, we prove that the spectrum consists of the perturbative eigenvalues $\\{E_n(\\beta)\\}_{n\\geq 0}$ labeled by the constant number $n$ of nodes of the corresponding eigenfunctions. In addition, for all $\\beta\\in\\C_c$, $E_n(\\beta)$ can be computed as the Stieltjes-Pad\\'e sum of its perturbation series at $\\beta=0$. This also gives an alternative proof of the fact that the spectrum of $H(\\beta"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.2797","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"}