Flux continuity and probability conservation in complexified Bohmian mechanics
Bill Poirier

Recent years have seen increased interest in complexified Bohmian mechanical trajectory calculations for quantum systems, both as a pedagogical and computational tool. In the latter context, it is {\em essential} that trajectories satisfy probability conservation, to ensure they are always guided to where they are most needed. In this paper, probability conservation for complexified Bohmian trajectories is considered. The analysis relies on time-reversal symmetry considerations, leading to a generalized expression for the conjugation of wavefunctions of complexified variables. This in turn enables meaningful discussion of complexified flux continuity, which turns out {\em 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 {\em not} conserved along complex Bohmian trajectories.

© 2008 The American Physical Society.