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 -