Scattering potential
= Scattering potential
{title2=$V$}
For a refractive index $n(\mathbf r)$ and background wavenumber $k_0$, one sign convention defines the scattering potential by $V=k_0^2(1-n^2)$. The total field then satisfies $(\Delta+k_0^2)\psi=V\psi$.
The opposite convention $V=k_0^2(n^2-1)$ gives $(\Delta+k_0^2)\psi=-V\psi$ and reverses the sign attached to the corresponding Green-function integral. Either convention is valid when used consistently.