[QUE/QM-23020]

To the lowest non vanishing order in \(\epsilon\), compute the corrections to the
energy levels of the Hamiltonian
\begin{equation}
 H = H_0  + H^\prime
\end{equation}
for the case of spin 1, where
\begin{equation}
   H_0= \vec{S}^2 + S_z^2, \qquad H^\prime = \epsilon S_x
\end{equation}