TY - JOUR

T1 - Bohmian mechanics without pilot waves

AU - Poirier, Bill

N1 - Funding Information:
This work was supported by a grant from The Welch Foundation ( D-1523 ), and by a Small Grant for Exploratory Research from the National Science Foundation ( CHE-0741321 ). The author wishes to express gratitude to Alon Faraggi, Sheldon Goldstein, Marco Matone, Salvador Miret-Artés, Eli Pollak, Angel Sanz, Jeremy Schiff, David Tannor, Paul Werbos, and Robert Wyatt, for interesting discussions related to the present work.

PY - 2010/5/12

Y1 - 2010/5/12

N2 - In David Bohm's causal/trajectory interpretation of quantum mechanics, a physical system is regarded as consisting of both a particle and a wavefunction, where the latter "pilots" the trajectory evolution of the former. In this paper, we show that it is possible to discard the pilot wave concept altogether, thus developing a complete mathematical formulation of time-dependent quantum mechanics directly in terms of real-valued trajectories alone. Moreover, by introducing a kinematic definition of the quantum potential, a generalized action extremization principle can be derived. The latter places very severe a priori restrictions on the set of allowable theoretical structures for a dynamical theory, though this set is shown to include both classical mechanics and quantum mechanics as members. Beneficial numerical ramifications of the above, "trajectories only" approach are also discussed, in the context of simple benchmark applications.

AB - In David Bohm's causal/trajectory interpretation of quantum mechanics, a physical system is regarded as consisting of both a particle and a wavefunction, where the latter "pilots" the trajectory evolution of the former. In this paper, we show that it is possible to discard the pilot wave concept altogether, thus developing a complete mathematical formulation of time-dependent quantum mechanics directly in terms of real-valued trajectories alone. Moreover, by introducing a kinematic definition of the quantum potential, a generalized action extremization principle can be derived. The latter places very severe a priori restrictions on the set of allowable theoretical structures for a dynamical theory, though this set is shown to include both classical mechanics and quantum mechanics as members. Beneficial numerical ramifications of the above, "trajectories only" approach are also discussed, in the context of simple benchmark applications.

KW - Bohmian mechanics

KW - Interpretation of quantum mechanics

KW - Pilot wave

KW - Quantum trajectory methods

KW - Time-dependent quantum mechanics

KW - Trajectory formulation of quantum mechanics

UR - http://www.scopus.com/inward/record.url?scp=77953286271&partnerID=8YFLogxK

U2 - 10.1016/j.chemphys.2009.12.024

DO - 10.1016/j.chemphys.2009.12.024

M3 - Article

AN - SCOPUS:77953286271

SN - 0301-0104

VL - 370

SP - 4

EP - 14

JO - Chemical Physics

JF - Chemical Physics

IS - 1-3

ER -