{"paper":{"title":"High-energy asymptotics for finite-interval Schr\\\"odinger operators with Gaussian white-noise potential","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Wenwen Jian, Xiaoping Yuan, Yingdu Dong","submitted_at":"2026-06-21T10:24:54Z","abstract_excerpt":"We study the one-dimensional Schr\\\"odinger operator on a fixed interval with Gaussian white-noise potential, \\[\n  H_\\omega=-\\frac{\\dd^2}{\\dd x^2}+\\rho\\dot B_x(\\omega), \\] under Dirichlet boundary conditions. The operator is defined pathwise through the quasi-derivative realization of Sturm--Liouville operators with distributional potentials. Let $\\lambda_n$ be the Dirichlet eigenvalues, $\\lambda_n^+=\\max\\{\\lambda_n,0\\}$, and $k_n=\\sqrt{\\lambda_n^+}$. For every finite $p$, we prove the high-energy expansion \\[\n  k_n=\\frac{n\\pi}{L}\n  +\\frac{\\rho}{n\\pi}\\int_0^L\n  \\sin^2\\left(\\frac{n\\pi s}{L}\\righ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.22426","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.22426/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}