Transmission amplitude ($\psi \sim e^{i{k}_{L}X}+r{e}^{-i{k}_{L}X}(X\to -\infty ),\psi \sim t{e}^{i{k}_{R}X}(X\to +\infty )$)

For one-dimensional quantum scattering, $t$ is the complex amplitude of the outgoing transmitted wave relative to the incoming wave. The transmission probability is $|t{|}^2$ times the ratio of transmitted and incident flux velocities; with equal asymptotic dispersion it is $|t{|}^2$. A reflectionless potential has $r=0$ and a unit-modulus transmission amplitude whose phase shifts continuum quantization. The supersymmetric factorization of the one-soliton potential gives $t(k)=(k+im)/(k-im)$ for its single-bound-state potential.