{"paper":{"title":"Effective Hamiltonians for Constrained Quantum Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Jakob Wachsmuth, Stefan Teufel","submitted_at":"2009-07-02T11:55:48Z","abstract_excerpt":"We consider the time-dependent Schr\\\"odinger equation on a Riemannian manifold $\\mathcal{A}$ with a potential that localizes a certain class of states close to a fixed submanifold $\\mathcal{C}$. When we scale the potential in the directions normal to $\\mathcal{C}$ by a parameter $\\varepsilon\\ll 1$, the solutions concentrate in an $\\veps$-neighborhood of $\\mathcal{C}$. We derive an effective Schr\\\"odinger equation on the submanifold $\\mathcal{C}$ and show that its solutions, suitably lifted to $\\mathcal{A}$, approximate the solutions of the original equation on $\\mathcal{A}$ up to errors of ord"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0907.0351","kind":"arxiv","version":3},"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"}