Orbital-angular-momentum-squared perturbation of hydrogen
= Orbital-angular-momentum-squared perturbation of hydrogen
A perturbation $gL^2$ preserves the hydrogen eigenbasis and shifts $|n,\ell,m\rangle$ by
$$
g\hbar^2\ell(\ell+1).
$$
In the first excited eigenspace, the $2s$ state is unshifted and the three $2p$ states receive the common shift $2g\hbar^2$.