 Angular momentum eigenstate

A joint eigenstate $|j,m⟩$ of $J^2$ and $J_z$, with eigenvalues ${\hslash }^{2}j(j+1)$ and $\hslash m$. Its allowed labels satisfy $j\in \{0,1/2,1,\dots \}$ and $m=-j,-j+1,\dots ,j$.