Let the unperturbed atom or molecule be in a g -fold degenerate state with orthonormal zeroth-order state functions ψ ψ 1 0 , … … , ψ ψ g 0 . (Non-degeneracy is the special case g = 1). According to perturbation theory the first-order energies are the eigenvalues of the g × g matrix with general element ( V i n t ) k l = ⟨ ⟨ ψ ψ k 0 | V i n t | ψ ψ l 0 ⟩ ⟩ = − − F ⋅ ⋅ ⟨ ⟨ ψ ψ k 0 | μ μ | ψ ψ l 0 ⟩ ⟩ , k , l = 1 , … … , g . If g = 1 (as is often the case for electronic states of molecules) the first-order energy becomes proportional to the expectation (average) value of the dipole operator μ μ , E ( 1 ) = − − F ⋅ ⋅ ⟨ ⟨ ψ ψ 1 0 | μ μ | ψ ψ 1 0 ⟩ ⟩ = − − F ⋅ ⋅ ⟨ ⟨ μ μ ⟩ ⟩ .