Transmission through a potential barrier: T ≈ exp(−2∫κ dx)
0.801.502.00.20
In the WKB approximation, a particle with energy E tunnels through a barrier V(x)>E with transmission T ≈ exp(−2∫√(2m(V−E))/ℏ dx). The wavefunction decays exponentially inside the classically forbidden region, but leaks through — the basis of α-decay, scanning tunneling microscopy, and Josephson junctions.