 Quantum transmission

Quantum transmission is the passage of an incident quantum particle into an outgoing region through a specified interaction or potential. A wave function can have both reflected and transmitted components; the measurable transmission probability compares outgoing and incoming probability currents, rather than comparing wave amplitudes alone.

For a one-dimensional, constant-mass Schrödinger equation, write an incident amplitude of one and transmitted amplitude $t$, with positive asymptotic wavenumbers $k_L$ and $k_R$. The probability current givesOnly when the asymptotic wavenumbers agree does this become $|t{|}^2$. A real, static potential with no additional loss channels has reflection plus transmission probability equal to one. Quantum tunnelling is an important case in which the transmitted component crosses a region forbidden by the corresponding classical energy condition.