Above we have made the electric dipole approximation in which the spatial dependence of the field is neglected. The Heisenberg equation for a k λ is found similarly from the Hamiltonian to be: a ˙ ˙ k λ λ = i ω ω k a k λ λ + i e 2 π π ℏ ℏ ω ω k V x ˙ ˙ ⋅ ⋅ e k λ λ in the electric dipole approximation.