= Linear confinement correction to Coulomb bound states
{title2=$\Delta E_{nl}=b\langle r\rangle_{nl}$}
For <reduced mass> $\mu$ and Coulomb strength $a$, put $a_q=\hbar^2/(\mu a)$. The perturbation $br$ shifts the $1s,2s,2p$ energies by $3ba_q/2,6ba_q,5ba_q$, respectively. These values follow by integrating $r^3|R_{nl}|^2$. Because the perturbation is central, angular <orthogonality> makes its <matrix> diagonal inside each Coulomb <energy> <eigenspace>. It splits the accidental degeneracy between different orbital angular momenta while preserving magnetic degeneracy.
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