  In recent years, intensive effort has gone into developing numerical tools
for exact quantum mechanical calculations that are based on Bohmian mechanics.
As part of this effort we have recently developed as alternative formulation of
Bohmian mechanics in which the quantum action, S, is taken to be complex [JCP
{125}, 231103 (2006)]. In the alternative formulation there is a significant
reduction in the magnitude of the quantum force as compared with the
conventional Bohmian formulation, at the price of propagating complex
trajectories. In this paper we show that Bohmian mechanics with complex action
is able to overcome the main computational limitation of conventional Bohmian
methods -- the propagation of wavefunctions once nodes set in. In the vicinity
of nodes, the quantum force in conventional Bohmian formulations exhibits rapid
oscillations that pose severe difficulties for existing numerical schemes. We
show that within complex Bohmian mechanics, multiple complex initial conditions
can lead to the same real final position, allowing for the description of nodes
as a sum of the contribution from two or more crossing trajectories. The idea
is illustrated on the reflection amplitude from a one-dimensional Eckart
barrier. We believe that trajectory crossing, although in contradiction to the
conventional Bohmian trajectory interpretation, provides an important new tool
for dealing with the nodal problem in Bohmian methods.
