= Evanescent amplitude versus transmitted current
{title2=$j[Te^{-\alpha x}]=0$}
For a real positive decay coefficient alpha, a stationary exponential tail has zero <probability current> because $\operatorname{Im}(\psi^*\partial_x\psi)=0$. Matching a subthreshold <potential step> can nevertheless give a nonzero coefficient T with $|T|^2>1$ relative to a unit incident plane-wave amplitude. This measures the density just beyond the step, not a flux-transmission probability. It describes penetration without a propagating outgoing channel in the semi-infinite high-potential region.
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