An evanescent wave is a non-propagating wave with an imaginary wave vector. In this study, we prove that these are solutions of the tachyon-like Klein–Gordon equation, and that in the tunneling of ultrarelativistic spin-1/2 particles they describe superluminal states arising from interactions between a particle and barrier. These states decay as a particle emerges from the opposite side of a potential barrier, conserving the same initial energy but not necessarily the same mass. The obtained theory is applied to the neutrino, to explain flavor oscillations during free flight and determine the conditions that maximize the probability of their occurrence.