When one changes the basis to the eigenvectors of the Hamiltonian, in other words, if the basis states | 1 ⟩ , | 2 ⟩ {\displaystyle |1\rangle ,|2\rangle } are chosen to be the eigenvectors then ϵ 1 = H 11 = ⟨ 1 | H | 1 ⟩ = E 1 ⟨ 1 | 1 ⟩ = E 1 {\displaystyle \epsilon _{1}=H_{11}=\langle 1|H|1\rangle =E_{1}\langle 1|1\rangle =E_{1}} and β + i γ = H 21 = ⟨ 2 | H | 1 ⟩ = E 1 ⟨ 2 | 1 ⟩ = 0 {\displaystyle \beta +i\gamma =H_{21}=\langle 2|H|1\rangle =E_{1}\langle 2|1\rangle =0} and so the Hamiltonian is diagonal, i.e. | r | = δ {\displaystyle |\mathbf {r} |=\delta } and is of the form,