 Spin projection

The spin projection is the component of a particle's spin angular momentum along a specified spatial direction. For the $z$ direction, an eigenstate of the angular momentum operator $S_z$ has measured value $m_s\hslash$, where $m_s=-s,-s+1,\dots ,s$ and $\hslash$ is the reduced Planck constant. For spin one-half, the two possible results are $+\hslash /2$ and $-\hslash /2$.

The direction belongs to the measurement arrangement: a state with definite $S_z$ generally has uncertain $S_x$. A Stern-Gerlach experiment separates the corresponding components through a spatially varying magnetic field. This is a component measurement, rather than a claim that the full spin angular momentum points along one of two classical directions.