{"paper":{"title":"Non-differentiable Bohmian trajectories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"Gebhard Gruebl, Markus Penz","submitted_at":"2010-11-12T09:09:51Z","abstract_excerpt":"A solution $\\psi $ to Schr\\\"odinger's equation needs some degree of regularity in order to allow the construction of a Bohmian mechanics from the integral curves of the velocity field $\\hbar \\Im \\left( \\bigtriangledown \\psi /m\\psi \\right) .$ In the case of one specific non-differentiable weak solution $\\Psi $ we show how Bohmian trajectories can be obtained for $\\Psi $ from the trajectories of a sequence $\\Psi_{n}\\rightarrow \\Psi.$ (For any real $t$ the sequence $\\Psi_{n}\\left( t,\\cdot \\right) $ converges strongly.) The limiting trajectories no longer need to be differentiable. This suggests a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.2852","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"}