S ^ j = ( S ^ j x , S ^ j y , S ^ j z ) = ℏ 2 ( σ ^ x , σ ^ y , σ ^ z ) {\displaystyle {\hat {\mathbf {S} }}_{j}=({\hat {S}}_{j}^{x},{\hat {S}}_{j}^{y},{\hat {S}}_{j}^{z})={\frac {\hbar }{2}}({\hat {\sigma }}_{x},{\hat {\sigma }}_{y},{\hat {\sigma }}_{z})} ( σ ^ x , σ ^ y , σ ^ z ) {\displaystyle ({\hat {\sigma }}_{x},{\hat {\sigma }}_{y},{\hat {\sigma }}_{z})}