---
abstract: 'In a previous paper \[J. Chem. Phys. [**121**]{} 4501 (2004)\] a unique bipolar decomposition, $\Psi = \Psi_1 + \Psi_2$ was presented for stationary bound states $\Psi$ of the one-dimensional  equation, such that the components $\Psi_1$ and $\Psi_2$ approach their semiclassical WKB analogs in the large action limit. Moreover, by applying the Madelung-Bohm ansatz to the components rather than to $\Psi$ itself, the resultant bipolar Bohmian mechanical formulation satisfies the correspondence principle. As a result, the bipolar quantum trajectories are classical-like and well-behaved, even when $\Psi$ has many nodes, or is wildly oscillatory. In this paper, the previous decomposition scheme is modified in order to achieve the same desirable properties for stationary scattering states. Discontinuous potential systems are considered (hard wall, step, square barrier/well), for which the bipolar quantum potential is found to be [*zero*]{} everywhere, except at the discontinuities. This approach leads to an exact numerical method for computing stationary scattering states of any desired boundary conditions, and reflection and transmission probabilities. The continuous potential case will be considered in a future publication.'
author:
- Corey Trahan and Bill Poirier
title: |
    Reconciling Semiclassical and Bohmian Mechanics:\
    II. Scattering states for discontinuous potentials
---

INTRODUCTION {#intro}
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Much 