where ω = μ B / ℏ {\displaystyle \omega =\mu B/\hbar } and e i ω t σ ⋅ n ^ = cos ⁡ ( ω t ) I + i n ^ ⋅ σ sin ⁡ ( ω t ) {\displaystyle e^{i\omega t{\boldsymbol {\sigma }}\cdot \mathbf {\hat {n}} }=\cos {\left(\omega t\right)}I+i\;\mathbf {\hat {n}} \cdot {\boldsymbol {\sigma }}\sin {\left(\omega t\right)}} . Physically, this corresponds to the Bloch vector precessing around n ^ {\displaystyle \mathbf {\hat {n}} } with angular frequency 2 ω {\displaystyle 2\omega } . Without loss of generality, assume the field is uniform points in z ^ {\displaystyle \mathbf {\hat {z}} } , so that the time evolution operator is given as