{"paper":{"title":"Virtual bound levels in a gap of the essential spectrum of the Schroedinger operator with a weakly perturbed periodic potential","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Leonid Zelenko","submitted_at":"2015-05-27T15:39:35Z","abstract_excerpt":"In the space $L_2(R^d)$ we consider the Schr\\\"odinger operator $H_\\gamma=-\\Delta+ V(x)\\cdot+\\gamma W(x)\\cdot$, where $V(x)=V(x_1,x_2,\\dots,x_d)$ is a periodic function with respect to all the variables, $\\gamma$ is a small real coupling constant and the perturbation $W(x)$ tends to zero sufficiently fast as $|x|\\rightarrow\\infty$. We study so called virtual bound levels of the operator $H_\\gamma$, that is those eigenvalues of $H_\\gamma$ which are born at the moment $\\gamma=0$ in a gap $(\\lambda_-,\\,\\lambda_+)$ of the spectrum of the unperturbed operator $H_0=-\\Delta+ V(x)\\cdot$ from an edge of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.07381","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"}