even real-valued, and there are generally two linearly independent solutions of interest for each $E$, instead of just one. Condition (1) above poses no difficulty for $\Ppm(x)$, as these component functions are non-$L^2$ and complex-valued, even in the bound eigenstate case. In principle, condition (2) is not difficult either; although the flux value depends on the normalization of $\Psi$ itself, which is not $L^2$, certain well-established normalization conventions for scattering states exist, that can be applied equally well to semiclassical and exact quantum solutions. There is no action median [*per se*]{} for scattering states, as the action enclosed within the $\Psi_+(x)$ and $\Psi_-(x)$ phase space Lagrangian manifolds[@poirier04bohmI; @keller60; @maslov; @littlejohn92] (LMs) is infinite; however, the scattering analog of condition (3) is related to the asymptotic boundary conditions, and it is here that one encounters difficulty. Moreover, an additional concern is raised by the doubly-degenerate nature of the continuum eigenstates, namely: should each scattering $\Psi(x)$ have its [*own*]{} $\Ppm(x)$ decomposition, or should there be a single $\Ppm(x)$ pair, from which all degenerate $\Psi(x)$’s may be constructed via arbitrary linear superposition?

To resolve these issues, we will adopt the same general strategy used in paper I, i.e. we will resort to semiclassical 