{"paper":{"title":"Universal Lattice Basis","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["quant-ph"],"primary_cat":"physics.comp-ph","authors_text":"C.J. Tymczak, Jonathan Jerke","submitted_at":"2013-08-31T23:12:07Z","abstract_excerpt":"We report on the utility of using Shannons Sampling theorem to solve Quantum Mechanical systems. We show that by extending the logic of Shannons interpolation theorem we can define a Universal Lattice Basis, which has superior interpolating properties compared to traditional methods. This basis is orthonormal, semi-local, has a Euclidean norm, and a simple analytic expression for the derivatives. Additionally, we can define a bounded domain for which band-limited functions, such as Gaussians, show quadratic convergence in the representation error in respect to the sampling frequency. This theo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.0166","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"}