On the Global Existence of Bohmian Mechanics
K. Berndl, D. Dürr, S. Goldstein, G. Peruzzi, N. Zangh\`ı
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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