{"paper":{"title":"Completeness of Averaged Scattering Solutions and Inverse Scattering at a Fixed Energy","license":"","headline":"","cross_cats":["math.AP","math.MP"],"primary_cat":"math-ph","authors_text":"Ricardo Weder","submitted_at":"2005-10-13T17:55:54Z","abstract_excerpt":"We prove that the averaged scattering solutions to the Schr\\\"odinger equation with short-range electromagnetic potentials $(V,A)$ where $V(x)=O(|x|^{-\\rho}), A(x)= O(|x|^{-\\rho}), |x| \\to \\infty, \\rho >1,$ are dense in the set of all solutions to the Schr\\\"odinger equation that are in $L^2(K)$ where $K$ is any connected bounded open set in $\\ere^n,n\\geq 2,$ with smooth boundary.\n  We use this result to prove that if two short-range electromagnetic potentials $(V_1,A_1)$ and $(V_2,A_2)$ in $\\ere^n, n\\geq 3,$ have the same scattering matrix at a fixed positive energy and if the electric potentia"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0510050","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/math-ph/0510050/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"}