{"paper":{"title":"Schr\\\"odinger Equation on Fractals Curves Imbedding in $R^3$","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Alireza Khalili Golmankhaneh, Dumitru Baleanu","submitted_at":"2013-08-01T18:28:29Z","abstract_excerpt":"In this paper we have generalized the quantum mechanics on fractal time-space. The time is changing on Cantor-set like but space is considered as fractal curve like Von-Koch curve. The Feynman path method in quantum mechanics has been suggested on fractal curve. Using $F^{\\alpha}$-calculus and Feynman path method we found the Schr\\\"{e}dinger on fractal time-space. The Hamiltonian operator and momentum operator has been derived. More, the continuity equation and the probability density is given in generalized formulation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.0291","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"}