 Klein-Gordon step amplification

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.