On the global existence of Bohmian mechanics

TY - JOUR

T1 - On the global existence of Bohmian mechanics

AU - Berndl, K.

AU - Dürr, D.

AU - Goldstein, S.

AU - Peruzzi, G.

AU - Zanghì, N.

PY - 1995/11

Y1 - 1995/11

N2 - 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.

AB - 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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U2 - https://doi.org/10.1007/BF02101660

DO - https://doi.org/10.1007/BF02101660

M3 - Article

SN - 0010-3616

VL - 173

SP - 647

EP - 673

JO - Communications In Mathematical Physics

JF - Communications In Mathematical Physics

IS - 3

ER -