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A potential barrier is a region of higher potential energy separating accessible regions of a physical system. A classical particle cannot pass through a barrier higher than its total energy along its trajectory, but a quantum particle can have nonzero transmission probability through a finite barrier by quantum tunnelling.
In a one-dimensional region with constant , the Schrödinger equation gives exponential solutions with tunnelling decay constant . The wavefunction can therefore penetrate a finite barrier and match an outgoing wave on the other side. The rectangular potential barrier is an exactly solvable model; smooth barriers lead naturally to a semiclassical approximation. Even for , quantum reflection can occur where the potential changes.