The full second order solution The full second order solution includes the zeroth order terms as well Ca(t) = 1 - 2 Jo Hba(t')e -iwot' Hhalt" )elwot" at" at cb ( t ) = - / H'ba(t')elwot dt' This iterative solution can be continued for higher precision and in general, the /th order solution has / factors of H' note that while the exact coefficients, must be normalized, this approximate solution is only normalized to order /V in H' for example to first order, normalization becomes t 2 Ical2 + |cb/2 = 12 + - F. Hoa(t')elwot' dt' #1 o Carlo Segre (Illinois Tech) PHYS 406 - Fundamentals of Quantum Theory II Time dependent perturbationsGet the second-order and third-order terms in To (transition matrix element ) of Fermi's golden rule ar = [Ao + A'(x, 1)|4 Where 4 ( x, 1 ) = [ CK(1)$k(x)e-iExt k . Substitute to the time-dependent SE with interaction Hamiltonian: . Assume the perturbing Hamiltonian is small and constant such that ci(1) = 1 and Ck#i(1) = 0 (first-order approximation) YES def dt = -i( flA'Idei(Es-ED TA= (flA'li) of(T) = -iTfi pi(Ef-E))I dt Jo