reflection & transmission

When a quantum wave meets a step or barrier in the potential, it generally divides: part of it bounces back as a reflected wave, and part continues onward as a transmitted wave. The reflection coefficient and the transmission coefficient are the two numbers that record how the incoming wave splits — the fraction of probability that turns back and the fraction that goes through. Because probability is conserved, these two fractions must always add up to one.

This splitting is a thoroughly wave-like behaviour with no place in classical particle physics. A classical ball with enough energy always crosses a step and never reflects; one with too little always bounces and never crosses. Quantum mechanics blends both outcomes into probabilities. A particle with plenty of energy can still be reflected, and a particle with too little can still be transmitted by tunnelling. Which fractions you get depends on the particle's energy and the exact shape of the potential.

The two coefficients are the standard language of scattering, the branch of quantum mechanics concerned with how particles deflect, pass through, or bounce off the things they encounter. Measuring how a beam of particles reflects and transmits off a target is one of the primary ways physicists deduce the unseen forces and structures at work, from the layering inside a semiconductor device to the internal architecture of a proton.