As discussed above, in time-dependent perturbation theory one can simply drop terms from the lower bounds of

Question:

As discussed above, in time-dependent perturbation theory one can simply drop terms from the lower bounds of all time integrals except the final one, and add a small imaginary term in the denominator consistent with causality. Show that following this procedure for the real part of the third order of the expansion (8.1.4) gives the same third-order term as time-independent Rayleigh–Schrödinger theory,