The following paraphrases the treatment of Cohen-Tannoudji. As before, the total Hamiltonian is the sum of an “original” Hamiltonian H 0 and a perturbation: H = H 0 + H ′ . We can still expand an arbitrary quantum state’s time evolution in terms of energy eigenstates of the unperturbed system, but these now consist of discrete states and continuum states. We assume that the interactions depend on the energy of the continuum state, but not any other quantum numbers. The expansion in the relevant states in the Dirac picture is | ψ ψ ( t ) ⟩ ⟩ = a i e − − i ω ω i t | i ⟩ ⟩ + ∫ ∫ C d ε ε a ε ε e − − i ω ω t | ε ε ⟩ ⟩ , where ω ω i = ε ε i / ℏ ℏ , ω ω = ε ε / ℏ ℏ and ε ε i , ε ε are the energies of states | i ⟩ ⟩ , | ε ε ⟩ ⟩ , respectively. The integral is over the continuum ε ε ∈ ∈ C , i.e. | ε ε ⟩ ⟩ is in the continuum.