The vector r {\displaystyle \mathbf {r} } is given by ( β , γ , δ ) {\displaystyle (\beta ,\gamma ,\delta )} and σ {\displaystyle \sigma } is given by ( σ 1 , σ 2 , σ 3 ) {\displaystyle (\sigma _{1},\sigma _{2},\sigma _{3})} . This representation simplifies the analysis of the time evolution of the system and is easier to use with other specialized representations such as the Bloch sphere.