In deriving the interaction Hamiltonian for a free electron scattering from a localized electron, we showed that
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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.
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thus the S matrix is where The interaction Hamiltonian is given as with Vint v2kko bre kK...View the full answer
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