2004/06/15 by Stefan Teufel, Roderich Tumulka · 3 citations
Arts and Humanities · Mathematics · Physics and Astronomy · #Philosophy and History of Science #Philosophy, Science, and History #Quantum Mechanics and Applications #math-ph #math.MP #msc:34A12 #msc:81P99 #quant-ph
paper · pdf · doi:10.1007/s00220-005-1302-0
published as Commun. Math. Phys. 258 (2005) 349-365 · 18 pages
arxiv created 2004/06/15 · openalex publication_date 2005/02/25 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We address the question whether Bohmian trajectories exist for all times. Bohmian trajectories are solutions of an ordinary differential equation involving a wavefunction obeying either the Schroedinger or the Dirac equation. Some trajectories may end in finite time, for example by running into a node of the wavefunction, where the law of motion is ill-defined. The aim is to show, under suitable assumptions on the initial wavefunction and the potential, global existence of almost all solutions. We provide a simpler and more transparent proof of the known global existence result for spinless Schroedinger particles and extend the result to particles with spin, to the presence of magnetic fields, and to Dirac wavefunctions. Our main new result are conditions on the current vector field on configuration-space-time which are sufficient for almost-sure global existence.