evanescent wave

An evanescent wave is the part of a wavefunction that lives inside a classically forbidden region — a place where the particle's energy is less than the potential, so by classical rules it should never be found there. Rather than oscillating like an ordinary wave, the wavefunction in this region simply fades, dropping off exponentially with distance. It is a wave only in name; it carries no steady ripple, just a smooth, rapid decline toward zero.

This decaying tail is the secret engine behind tunnelling. When a wave meets a barrier too high to climb, it becomes evanescent inside the barrier instead of stopping dead. If the barrier is thin, the tail has not yet decayed to nothing by the time it reaches the far side, so a small oscillating wave re-emerges beyond. The shorter the forbidden region, the more of the evanescent wave survives, and the greater the chance of tunnelling through.

Evanescent waves are not unique to quantum mechanics; the same mathematics governs light. When light undergoes total internal reflection in a prism, an evanescent field reaches a tiny distance beyond the surface, and a second prism brought close enough can pick it up — the optical twin of tunnelling. In both cases the lesson is the same: a wave does not vanish abruptly at a forbidden edge but leaks a short, fading distance beyond it.