+These equations can be simplified to read
+\begin{eqnarray}
+\ldots
+\text{ .}
+\end{eqnarray}
+
+\subsubsection{A different basis set}
+
+The above basis is composed of eigenfunctions
+\begin{equation}
+\ket{l,m} \text{, } \ket{\pm} \text{ of operators }
+L^2\text{, } L_z \text{ and } S_z
+\text{.}
+\end{equation}
+These eigenfunctions diagonalize the scalar relativistic Hamiltonian.
+Introducing spin-orbit interaction, however, it is a good idea to chose eigenfunctions that diagonalize the perturbation
+\begin{equation}
+L\cdot S=\frac{1}{2}(J^2-L^2-S^2)
+\text{ ,}
+\end{equation}
+i.e.\ simultaneous eigenfunctions of $J^2$, $L^2$ and $S^2$.