  In a previous paper [J. Chem. Phys. 121 4501 (2004)] a unique bipolar
decomposition, Psi = Psi1 + Psi2 was presented for stationary bound states Psi
of the one-dimensional Schroedinger equation, such that the components Psi1 and
Psi2 approach their semiclassical WKB analogs in the large action limit. The
corresponding bipolar quantum trajectories, as defined in the usual Bohmian
mechanical formulation, are classical-like and well-behaved, even when Psi has
many nodes, or is wildly oscillatory. A modification for discontinuous
potential stationary stattering states was presented in a second paper [J.
Chem. Phys. 124 034115 (2006)], whose generalization for continuous potentials
is given here. The result is an exact quantum scattering methodology using
classical trajectories. For additional convenience in handling the tunneling
case, a constant velocity trajectory version is also developed.
