= Klein-Gordon step amplification
{c}
{title2=$\mathcal R=(k+Q)^2/(k-Q)^2,\quad\mathcal T=-4kQ/(k-Q)^2$}
For the outgoing negative-energy branch $q=-Q$, matching the field and its spatial derivative gives these signed charge-current ratios. Their sum is one although reflection exceeds one. The ideal sharp step has a singular stationary matching denominator at $E=V_0/2$ in the supercritical range. It is not a finite single-particle <probability> prediction; wavepackets, source preparation and field quantization matter for its physical interpretation.
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