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On the global existence of Bohmian mechanics

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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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Authors and Affiliations

  1. Mathematisches Institut der Universität München, Theresienstraße 39, D-80333, München, Germany

    K. Berndl & D. Dürr

  2. Department of Mathematics, Rutgers University, 08903, New Brunswick, NJ, USA

    S. Goldstein

  3. Sezione INFN Firenze, Largo Fermi 2, I-50125, Firenze, Italy

    G. Peruzzi

  4. Dipartimento di Fisica, Università di Genova, Sezione INFN Genova, Via Dodecaneso 33, I-16146, Genova, Italy

    N. Zanghì

Authors
  1. K. Berndl
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  2. D. Dürr
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  3. S. Goldstein
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  4. G. Peruzzi
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  5. N. Zanghì
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Communicated by J. Lebowitz

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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

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