Stern-Gerlach spin measurement
= Stern-Gerlach spin measurement
{c}
{title2=$P_\pm=(I\pm\mathbf n\cdot\boldsymbol\sigma)/2$}
The ideal <projective measurement> of a spin-one-half component along a unit axis $\mathbf n$. The two outcomes have <Born rule> <probabilities> $\langle\psi|P_\pm|\psi\rangle$. For an input with <Bloch vector> $\mathbf r$, they are $(1\pm\mathbf n\cdot\mathbf r)/2$. This model distinguishes a mathematical <spin> measurement from engineering a literal free-electron beam splitter.