taking the inner product with each of e i ω ω 1 t ⟨ ⟨ 1 | and e i ω ω 2 t ⟨ ⟨ 2 | , and using the orthogonality condition of eigenstates ⟨ ⟨ i | j ⟩ ⟩ = δ δ i , j , we arrive at two equations in the coefficients c 1 ( t ) and c 2 ( t ) :