arXiv:0706.3508

We present a unified derivation of Bohmian methods that serves as a common
starting point for the derivative propagation method (DPM), Bohmian
mechanics with complex action (BOMCA), and the zero-velocity complex
action method (ZEVCA). The unified derivation begins with the ansatz
*ψ=e ^{iS}* where the action (S) is taken to be complex,
and the quantum force is obtained by writing a hierarchy of equations
of motion for the phase partial derivatives. We demonstrate how different
choices of the trajectory velocity field yield different formulations
such as DPM, BOMCA, and ZEVCA. The new derivation is used for two purposes.
First, it serves as a common basis for comparing the role of the quantum
force in the DPM and BOMCA formulations. Second, we use the new derivation
to show that superposing the contributions of real, crossing trajectories
yields a nodal pattern essentially identical to that of the exact quantum
wavefunction. The latter result suggests a promising new approach to deal
with the challenging problem of nodes in Bohmian mechanics.