The components of ψ ( t ) {\displaystyle \psi (t)} on the Bloch sphere will simply be R = ( cos ⁡ 2 ω t , − sin ⁡ 2 ω t , 0 ) {\displaystyle \mathbf {R} =\left(\cos {2\omega t},-\sin {2\omega t},0\right)} . This is a unit vector that begins pointing along x ^ {\displaystyle \mathbf {\hat {x}} } and precesses around z ^ {\displaystyle \mathbf {\hat {z}} } in a left-handed manner. In general, by a rotation around z ^ {\displaystyle \mathbf {\hat {z}} } , any state vector ψ ( 0 ) {\displaystyle \psi (0)} can be represented as a | ↑ ⟩ + b | ↓ ⟩ {\displaystyle a\left|\uparrow \right\rangle +b\left|\downarrow \right\rangle } with real coefficients a {\displaystyle a} and b {\displaystyle b} .