Let $V\in C_c^\infty(\mathbb R^3;\mathbb R)$, let $k\in\mathbb R^3\setminus\{0\}$, and assume the outgoing boundary value of the resolvent at $E_k=\hbar^2|k|^2/(2m)$ is well-defined on the source terms considered. A generalized outgoing scattering state at energy $E_k$ satisfies \begin{align*} \psi_k^{(+)}(x) &= e^{ik\cdot x} - \frac{2m}{\hbar^2}\int_{\mathbb R^3} G_k^{(+)}(x-y)V(y)\psi_k^{(+)}(y)\,d\mathcal L^3(y), \end{align*} where \begin{align*} G_k^{(+)}(x) = \frac{e^{i|k||x|}}{4\pi |x|} \end{align*} is the outgoing Green function for $-\Delta-|k|^2$ in $\mathbb R^3$.