Question: In deriving the interaction Hamiltonian for a free electron scattering from a localized electron, we showed that momentum conservation does not hold in the scattering

In deriving the interaction Hamiltonian for a free electron scattering from a localized electron, we showed that momentum conservation does not hold in the scattering process, and therefore an extra sum must be performed over all possible outgoing momenta. Show, following the same procedure as used to deduce (8.6.25), that energy is conserved at a vertex, by explicitly writing down the S-matrix for elastic scattering in time-dependent perturbation theory. 5(1)(t, to) = -iMaa ih. b b ith So 93 93 92

5(1)(t, to) = -iMaa ih. b b ith So 93 93 92 91 dt e-i(@1-02-03)t1 (8.6.25)

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