2010/11/12 by Gebhard Gruebl, Markus Penz, Gruebl, Gebhard +1
Arts and Humanities · Mathematics · Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #Opinion Dynamics and Social Influence #Philosophy and History of Science #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #math-ph #math.MP #quant-ph
paper · pdf · doi:10.48550/arxiv.1011.2852
12 pages, 4 figures; published in the monography 'Quantum Trajectories', Editor P K Chattaraj , Taylor & Francis, Boca Raton, November 1st, 2010
arxiv created 2010/11/12 · openalex publication_date 2010/11/12 · arxiv updated 2010/11/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A solution ψ to Schrödinger'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 ℏ \Im ( \bigtriangledown ψ/mψ) . In the case of one specific non-differentiable weak solution Ψ we show how Bohmian trajectories can be obtained for Ψ from the trajectories of a sequence Ψn→ Ψ. (For any real t the sequence Ψn( t,⋅ ) converges strongly.) The limiting trajectories no longer need to be differentiable. This suggests a way how Bohmian mechanics might work for arbitrary initial vectors Ψ in the Hilbert space on which the Schrödinger evolution % Ψ↦ e-ihtΨ acts.