The representation on the Bloch sphere for a state vector ψ ( 0 ) {\displaystyle \psi (0)} will simply be the vector of expectation values R = ( ⟨ σ x ⟩ , ⟨ σ y ⟩ , ⟨ σ z ⟩ ) {\displaystyle \mathbf {R} =\left(\langle \sigma _{x}\rangle ,\langle \sigma _{y}\rangle ,\langle \sigma _{z}\rangle \right)} . As an example, consider a state vector ψ ( 0 ) {\displaystyle \psi (0)} that is a normalized superposition of | ↑ ⟩ {\displaystyle \left|\uparrow \right\rangle } and | ↓ ⟩ {\displaystyle \left|\downarrow \right\rangle } , that is, a vector that can be represented in the σ z {\displaystyle \sigma _{z}} basis as