Angular momentum quantum number ($j$)

Labels an angular momentum eigenstate through the eigenvalue ${\hslash }^{2}j(j+1)$ of the squared angular momentum operator. The allowed projections are $m\hslash$, with $m=-j,\dots ,j$. Orbital angular momentum has integer $j$; spin can also have half-integer $j$.

The nonnegative integer $l$ for which a spherical harmonic has squared orbital angular momentum ${\hslash }^{2}l(l+1)$. The angular part of a regular scalar wavefunction has $l=0,1,2,\dots$ and magnetic quantum number $m=-l,\dots ,l$.