In physics, quantum tunnel ling, barrier penetration, or simply tunnel ling is a quantum mechanical phenomenon in which an object such as an electron or atom passes through a potential energy barrier that, according to classical mechanics, should not be passable due to the object not having sufficient energy to pass or surmount the barrier.
Tunnelling is a consequence of the wave nature of matter and quantum indeterminacy. The quantum wave function describes the states of a particle or other physical system and wave equations such as the Schrödinger equation describe their evolution. In a system with a short, narrow potential barrier, a small part of wavefunction can appear outside of the barrier representing a probability for tunnel ling through the barrier.
Since the probability of transmission of a wave packet through a barrier decreases exponentially with the barrier height, the barrier width, and the tunnel ling particle’s mass, tunnel ling is seen most prominently in low-mass particles such as electrons tunnel ling through atomically narrow barriers. However tunnel ling has been observed with protons and even atoms and tunnel ling has been used to explain physical effects with particles this large.









