A potential $u = u(x)$ that decays rapidly to zero as $|x| \to \infty$ is completely determined by its scattering data $S = \{\{\kappa_n, c_n\}_{n=1}^N, R(k)\}$. Given such scattering data, define \begin{align*} F(x) = \sum_{n=1}^N c_n^2 e^{-\kappa_n x} + \frac{1}{2\pi} \int_{-\infty}^\infty e^{ikx} R(k) \, dk, \end{align*} and let $K(x, y)$ be the unique solution to the **Gelfand–Levitan–Marchenko (GLM) integral equation** \begin{align*} K(x, y) + F(x + y) + \int_x^\infty K(x, z) F(z + y) \, dz = 0, \qquad y > x. \end{align*} Then the potential is recovered by \begin{align*} u(x) = -2\frac{d}{dx} K(x, x). \end{align*}