User:Sansern

where ${\widehat{\mathbf{𝐒}}}_j=({\hat{S}}_j^x,{\hat{S}}_j^y,{\hat{S}}_j^z)=\frac{\hslash }{2}({\hat{\sigma }}_x,{\hat{\sigma }}_y,{\hat{\sigma }}_z)$ is the vector operator for spin-1/2 with $({\hat{\sigma }}_x,{\hat{\sigma }}_y,{\hat{\sigma }}_z)$ being the vector of the Pauli matrices.