If the two-state system's time-independent Hamiltonian H {\displaystyle H} is defined as above, then its eigenvalues are given by E ± = α ± | r | {\displaystyle E_{\pm }=\alpha \pm |\mathbf {r} |} . Evidently α {\displaystyle \alpha } is the average energy of the two levels, and the norm of r {\displaystyle \mathbf {r} } is the splitting between them. The corresponding eigenvectors are denoted | + ⟩ {\displaystyle |+\rangle } and | − ⟩ {\displaystyle |-\rangle } .