Consider a photon which is scattered by a matter elastically. In an elastic scattering we have [itex]
|k_i|=|k_f| and k_f - k_i = G
[/itex] where [itex]
G
[/itex] is a reciprocal vector. But according to momentum conservation, the matter must obtain a momentum [itex]
\hbar G
[/itex] and hence the kinetic energy, so according to energy conservation we no longer have [itex]
|k_i|=|k_f|
[/itex] because some of the energy of incident photon is transferred to the matter and this is a contradiction!
|k_i|=|k_f| and k_f - k_i = G
[/itex] where [itex]
G
[/itex] is a reciprocal vector. But according to momentum conservation, the matter must obtain a momentum [itex]
\hbar G
[/itex] and hence the kinetic energy, so according to energy conservation we no longer have [itex]
|k_i|=|k_f|
[/itex] because some of the energy of incident photon is transferred to the matter and this is a contradiction!
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