\begin{equation}
R^S\propto -\left[\frac{\partial}{\partial r}+\frac{\left(1+\kappa^L\right)}{r}\right]R^{\alpha}_l
= \sqrt{\alpha\left(2l+3\right)}R^{\alpha}_{l+1}-2\sqrt{\frac{\alpha}{2l+1}}R^{\alpha}_{l-1}


\end{equation}