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,

(m| Vint m') (m' Vinti) (Ei Em)(Ei - Em') 4,(3) 40 =(i\Vintm). m,m' fi m/i - (i|Vint/m) - - (m/Vinti) (i Vinti) (Ei - Em) (8.1.28)