Using the above equation for E RR (t) we obtain an equation for the Heisenberg-picture operator x ( t ) that is formally the same as the classical equation for a linear dipole oscillator: x ¨ ¨ + ω ω 0 2 x − − τ τ x . . . = e m E 0 ( t ) where τ = ⁠ 2 e / 3 mc ⁠. in this instance we have considered a dipole in the vacuum, without any "external" field acting on it. the role of the external field in the above equation is played by the vacuum electric field acting on the dipole.