For simplicity consider a two-level atomic system with ground and excited states | g ⟩ ⟩ and | e ⟩ ⟩ , respectively (using the Dirac bracket notation). Let the energy difference between the states be ℏ ℏ ω ω 0 so that ω ω 0 is the transition frequency of the system. Then the unperturbed Hamiltonian of the atom can be written as