{"paper":{"title":"Error analysis of splitting methods for the time dependent Schrodinger equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.comp-ph"],"primary_cat":"math.NA","authors_text":"Ander Murua, Fernando Casas, Sergio Blanes","submitted_at":"2010-05-25T21:53:48Z","abstract_excerpt":"A typical procedure to integrate numerically the time dependent Schr\\\"o\\-din\\-ger equation involves two stages. In the first one carries out a space discretization of the continuous problem. This results in the linear system of differential equations $i du/dt = H u$, where $H$ is a real symmetric matrix, whose solution with initial value $u(0) = u_0 \\in \\mathbb{C}^N$ is given by $u(t) = \\e^{-i t H} u_0$. Usually, this exponential matrix is expensive to evaluate, so that time stepping methods to construct approximations to $u$ from time $t_n$ to $t_{n+1}$ are considered in the second phase of t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.4709","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"}