Abstract
We show that the particle motion in Bohmian mechanics, given by the solution of an ordinary differential equation, exists globally: For a large class of potentials the singularities of the velocity field and infinity will not be reached in finite time for typical initial values. A substantial part of the analysis is based on the probabilistic significance of the quantum flux. We elucidate the connection between the conditions necessary for global existence and the self-adjointness of the Schrödinger Hamiltonian.
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Berndl, K., Dürr, D., Goldstein, S. et al. On the global existence of Bohmian mechanics. Commun.Math. Phys. 173, 647–673 (1995). https://doi.org/10.1007/BF02101660
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DOI: https://doi.org/10.1007/BF02101660