Spatial Wavefunctions of Spin

We present an equivalent formulation of quantum mechanical angular momentum, based on spatial wavefunctions that depend on the Euler angles $\phi$,$\theta$,$\chi$. The wavefunctions are Wigner D-functions $D_{n m}^j (\phi,\theta,\chi)$, that have a body-fixed projection quantum number $n$, in addition to the usual $j$ and $m$ quantum numbers. Unusually, $n$ can have the value $(j+1/2)$. The states $D_{(S+1/2)~ m}^S (\phi,\theta,\chi)$ give a gyromagnetic ratio of $g=2$ for all $S>0$, and we identify these as the spatial wavefunctions of known fundamental charged particles with spin.