{"paper":{"title":"The spectrum of a Harmonic Oscillator Operator Perturbed by Point Interactions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.SP","authors_text":"Boris Mityagin","submitted_at":"2014-07-15T21:39:59Z","abstract_excerpt":"We consider the operator $ L = - (d/dx)^2 + x^2 y + w(x) y , y \\in L^2(\\mathbb{R}) $, where $ w(x) = s [ \\delta(x - b) - \\delta(x + b)], b \\neq 0,$ real, $s \\in \\mathbb{C}$. This operator has a discrete spectrum: eventually the eigenvalues are simple and $\\lambda_n = (2n + 1) + s^2 (\\kappa(n) / n) + \\rho(n)$, where $ \\kappa(n) = \\frac{1}{2\\pi} [(-1)^{n + 1} \\sin ( 2 b \\sqrt{2n} ) - \\frac{1}{2} \\sin ( 4 b \\sqrt{2n} ) ]$ and $ |\\rho(n) | \\leq C (\\log n) / (n^{3/2})$ If $s = i \\gamma$, $\\gamma$ real, the number $T(\\gamma)$ of non-real eigenvalues is finite, and $T(\\gamma) \\leq [ C (1 + | \\gamma |"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.4153","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"}