= Solution
The reflection-one result describes a semi-infinite <potential step>, rather than a finite-width barrier. Define $k=\sqrt{2mE}/\hbar$ and $\kappa=\sqrt{2m(V_0-E)}/\hbar$. For $E>0$, take
$$
\phi(x)=\begin{cases}e^{ikx}+r e^{-ikx},&x<0,\\c e^{-\kappa x},&x>0.\end{cases}
$$
The growing exponential is excluded by boundedness as $x\to\infty$. Continuity of $\phi$ and $\phi'$ at the finite step gives $1+r=c$ and $ik(1-r)=-\kappa c$, hence
$$
\boxed{r=\frac{k-i\kappa}{k+i\kappa},\qquad c=\frac{2k}{k+i\kappa},\qquad R=|r|^2=1.}
$$
The <probability current> of the decaying tail is zero; the reflected and incident currents have equal magnitude. This agrees with the classical reflection coefficient even though the spatial wave function differs from a classical trajectory.
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