 Scattering potential

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.