Complex-extended Bohmian mechanics

Abstract

Complex-extended Bohmian mechanics is investigated by analytically continuing the wave function in polar form into the complex plane. We derive the complex-extended version of the quantum Hamilton-Jacobi equation and the continuity equation in Bohmian mechanics. Complex-extended Bohmian mechanics recovers the standard real-valued Bohmian mechanics on the real axis. The trajectories on the real axis are in accord with the standard real-valued Bohmian trajectories. The trajectories launched away from the real axis never intersect the real axis, and they display symmetry with respect to the real axis. Trajectories display hyperbolic deflection around nodes of the wave function in the complex plane. © 2010 American Institute of Physics.