see below - please note this is not \'compton scattering\' In Thomson scattering

Question

see below - please note this is not 'compton scattering'

In Thomson scattering a photon with propagation vector ki and polarization is scattered by a free electron with initial momentum Pi. After the scattering process the electron has momentum Pf. while the scattered photon has propagation vector kf and polarization . For convenience we can always transform to a frame where the initial momentum of the electron is Pi = 0. In that frame, the nonrelativistic QED Hamiltonian can be used as long as , where m is the rest mass of the electron. We will assume this to be the case. Show classically from conservation of free energy and momentum that if Pi = 0 then

Explanation / Answer

The general form for the electric field may be written as

   E(r,t) = ? E0 exp(i(k

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