Evanescent amplitude versus transmitted current ($j[T{e}^{-\alpha x}]=0$)

For a real positive decay coefficient alpha, a stationary exponential tail has zero probability current because $\mathrm{Im}({\psi }^{\ast }{\partial }_x\psi )=0$. 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.