{"paper":{"title":"Properties of Quantum Systems via Diagonalization of Transition Amplitudes I: Discretization Effects","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.quant-gas","hep-th","physics.comp-ph","quant-ph"],"primary_cat":"cond-mat.stat-mech","authors_text":"Aleksandar Belic, Aleksandar Bogojevic, Ivana Vidanovic","submitted_at":"2009-11-26T21:44:40Z","abstract_excerpt":"We analyze the method for calculation of properties of non-relativistic quantum systems based on exact diagonalization of space-discretized short-time evolution operators. In this paper we present a detailed analysis of the errors associated with space discretization. Approaches using direct diagonalization of real-space discretized Hamiltonians lead to polynomial errors in discretization spacing $\\Delta$. Here we show that the method based on the diagonalization of the short-time evolution operators leads to substantially smaller discretization errors, vanishing exponentially with $1/\\Delta^2"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.5145","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"}