On the Global Existence of Bohmian Mechanics

Details On the Global Existence of Bohmian Mechanics On the Global Existence of Bohmian Mechanics

1995-03-09

arxiv.org/abs/quant-ph/9503013v1

Commun.Math.Phys. 173 (1995) 647-674

Physics

Quantum Physics

35 pages, LaTex

Scientific paper

10.1007/BF02101660

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 Schr\"odinger Hamiltonian.

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