In the case of a direct bandgap semiconductor, the recombination of an electron and a hole generates a photon that has energy equal to the bandgap of the semiconductor, accounting for energy conservation. But in this case, as the electron and hole have the same momentum, 'K' there is no difference. But the generated photon does have a momentum. So how is the momentum conserved in the radiative recombination in the case of direct band gap semiconductors?
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The photon momentum is very small compared to crystal momenta. So it is there, but easily accounted for. – Jon Custer Nov 10 '23 at 16:54