Quantum tunnelling is the quantum mechanical phenomenon where a wavefunction can propagate through a potential barrier. The effect was predicted in the early 20th century. Its acceptance as a general physical phenomenon came mid-century. Quantum tunneling was developed from the study of radioactivity. Tunneling occurs with barriers of thickness around 1–3 nm and smaller.

The transmission through the barrier can be finite and depends exponentially on the barrier height and barrier width. The wavefunction may disappear on one side and reappear on the other side. The wavefunction and its first derivative are continuous. In steady-state, the probability flux in the forward direction is spatially uniform. No particle or wave is lost.

Tunneling cannot be directly perceived. Much of its understanding is shaped by the microscopic world, which classical mechanics cannot explain. To understand the phenomenon, particles attempting to travel across a potential barrier can be compared to a ball trying to roll over a hill.

Quantum mechanics and classical mechanics differ in their treatment of this scenario. Classical mechanics predicts that particles that do not have enough energy to classically surmount a barrier cannot reach the other side.

Thus, a ball without sufficient energy to surmount the hill would roll back down. A ball that lacks the energy to penetrate a wall bounces back. Alternatively, the ball might become part of the wall (absorption).

In quantum mechanics, these particles can, with a small probability, tunnel to the other side, thus crossing the barrier. The ball, in a sense, borrows energy from its surroundings to cross the wall. It then repays the energy by making the reflected electrons more energetic than they otherwise would have been.

The reason for this difference comes from treating matter as having properties of waves and particles. One interpretation of this duality involves the Heisenberg uncertainty principle, which defines a limit on how precisely the position and the momentum of a particle can be simultaneously known. This implies that no solutions have a probability of exactly zero (or one), though it may approach infinity.

If, for example, the calculation for its position was taken as a probability of 1, its speed, would have to be infinity (an impossibility). Hence, the probability of a given particle’s existence on the opposite side of an intervening barrier is non-zero, and such particles will appear on the ‘other’ (a semantically difficult word in this instance) side in proportion to this probability.

Quantum tunneling plays an essential role in physical phenomena, such as nuclear fusion. It has applications in the tunnel diode, quantum computing, and in the scanning tunneling microscope.

Some physicists have claimed that it is possible for spin-zero particles to travel faster than the speed of light when tunneling. This apparently violates the principle of causality, since a frame of reference then exists in which the particle arrives before it has left.

In 1998, Francis E. Low reviewed briefly the phenomenon of zero-time tunneling. More recently, experimental tunneling time data of phonons, photons, and electrons was published by Günter Nimtz.

An experiment done in 2020, overseen by Aephraim Steinberg, showed that particles should be able to tunnel at apparent speeds faster than light.