\begin{equation}
\left[\begin{array}{c}R^L\chi_{\kappa,m}\\iR^S\chi_{-\kappa,m}\\\end{array}\right] = \frac{1}{r}\left[\begin{array}{c}P\chi_{\kappa,m}\\iQ\chi_{-\kappa,m}\\\end{array}\right]
\end{equation}