TY - JOUR

T1 - Flux continuity and probability conservation in complexified Bohmian mechanics

AU - Poirier, Bill

N1 - Copyright:
Copyright 2018 Elsevier B.V., All rights reserved.

PY - 2008/2/25

Y1 - 2008/2/25

N2 - Recent years have seen increased interest in complexified Bohmian mechanical trajectory calculations for quantum systems as both a pedagogical and computational tool. In the latter context, it is essential that trajectories satisfy probability conservation to ensure they are always guided to where they are most needed. We consider probability conservation for complexified Bohmian trajectories. The analysis relies on time-reversal symmetry considerations, leading to a generalized expression for the conjugation of wave functions of complexified variables. This in turn enables meaningful discussion of complexified flux continuity, which turns out not to be satisfied in general, though a related property is found to be true. The main conclusion, though, is that even under a weak interpretation, probability is not conserved along complex Bohmian trajectories.

AB - Recent years have seen increased interest in complexified Bohmian mechanical trajectory calculations for quantum systems as both a pedagogical and computational tool. In the latter context, it is essential that trajectories satisfy probability conservation to ensure they are always guided to where they are most needed. We consider probability conservation for complexified Bohmian trajectories. The analysis relies on time-reversal symmetry considerations, leading to a generalized expression for the conjugation of wave functions of complexified variables. This in turn enables meaningful discussion of complexified flux continuity, which turns out not to be satisfied in general, though a related property is found to be true. The main conclusion, though, is that even under a weak interpretation, probability is not conserved along complex Bohmian trajectories.

UR - http://www.scopus.com/inward/record.url?scp=40749144783&partnerID=8YFLogxK

U2 - 10.1103/PhysRevA.77.022114

DO - 10.1103/PhysRevA.77.022114

M3 - Article

AN - SCOPUS:40749144783

VL - 77

JO - Physical Review A - Atomic, Molecular, and Optical Physics

JF - Physical Review A - Atomic, Molecular, and Optical Physics

SN - 1050-2947

IS - 2

M1 - 022114

ER -