\begin{equation}
\left[ \frac{\vec{p}^2}{2m_e} + \frac{e^2 \vec{A}^2}{2m_e} + \frac{e}{2m_e}(\mathbf{l} + 2 \mathbf{s})
\cdot \vec{B} + V \right] \psi^L = i \hbar  \frac{\partial}{\partial t} \psi^L
\end{equation}