\begin{equation}
i \hbar \frac{\partial}{\partial t} \left( \begin{array}{c}
\psi^L \\
\psi^S \end{array} \right) = c  \left( \begin{array}{c}
(\vec{\sigma} \cdot \vec{\pi}) \psi^S \\
(\vec{\sigma} \cdot \vec{\pi}) \psi^L \end{array} \right)
+ m_ec^2  \left( \begin{array}{c}
 \psi^L \\
-\psi^S \end{array} \right) + V  \left( \begin{array}{c}
\psi^L \\
\psi^S \end{array} \right)
\end{equation}