The magnetic dipole transition Hamiltonian is
$\hat{H}=\frac{e}{2m_ec}\hat{\mathbf{B}}\cdot\hat{\mathbf{L}}$
How do I express it in terms of ladder operator $\hat{L}_+$, $\hat{L}_-$, and the $z$-projecttion angular momentum $L_z$?
I know that $\hat{L}_\pm=\hat{L}_x\pm i\hat{L}_y$. But is it possible to express that Hamiltonian in ladder operator of $\hat{L}_+$, $\hat{L}_-$, and $L_z$ without expressing $\hat{\mathbf{B}}$ in terms of ladder operator?