however since the $\hat{J}_i$ don't commute amongst themselves, $\hat{H}$ and only one of them (usually $\hat{J}_z$, with eigenvalue $m$) admit simultaneous eigenstates. Since the casimir $\sum_i \hat{J}_i^2$ (with eigenvalue $l(l+1)$) does commute with the $\hat{J}_i$ this gives is a further operator having the same eigenstates, so the simultaneous eigenfunctions are denoted $\psi_{n,m,l}$.