{"paper":{"title":"A uniqueness theorem for higher order anharmonic oscillators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Mikael Persson Sundqvist, S{\\o}ren Fournais","submitted_at":"2013-09-09T12:55:52Z","abstract_excerpt":"We study for $\\alpha\\in\\R$, $k \\in {\\mathbb N} \\setminus \\{0\\}$ the family of self-adjoint operators \\[ -\\frac{d^2}{dt^2}+\\Bigl(\\frac{t^{k+1}}{k+1}-\\alpha\\Bigr)^2 \\] in $L^2(\\R)$ and show that if $k$ is even then $\\alpha=0$ gives the unique minimum of the lowest eigenvalue of this family of operators. Combined with earlier results this gives that for any $k \\geq 1$, the lowest eigenvalue has a unique minimum as a function of $\\alpha$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.2141","kind":"arxiv","version":2},"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"}