Solution
= Solution
For $s=1/2$ and $\ell\ge1$, $j=\ell\pm1/2$. Their degeneracies are $2j+1=2\ell+2$ and $2\ell$, summing to $4\ell+2$ as before.
= Solution
For $s=1/2$ and $\ell\ge1$, $j=\ell\pm1/2$. Their degeneracies are $2j+1=2\ell+2$ and $2\ell$, summing to $4\ell+2$ as before.