{"paper":{"title":"Quantum Maupertuis Principle","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Antonia Karamatskou, Hagen Kleinert","submitted_at":"2011-02-12T07:55:24Z","abstract_excerpt":"According to the Maupertuis principle, the movement of a classical particle in an external potential $V(x)$ can be understood as the movement in a curved space with the metric $g_{\\mu\\nu}(x)=2M[V(x)-E]\\delta_{\\mu\\nu}$. We show that the principle can be extended to the quantum regime, i.e., we show that the wave function of the particle follows a Schr\\\"odinger equation in curved space where the kinetic operator is formed with the {\\it Weyl--invariant Laplace-Beltrami} operator. As an application, we use DeWitt's recursive semiclassical expansion of the time-evolution operator in curved space to"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.2486","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":""},"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"}