Let's consider an electron-positron pair with total spin equal to zero. When it annihilates it can not emit only one photon because it would have zero momentum and nonzero energy. The pair emits two photons with opposite momenta but on the momentum-energy plain it looks like the particle goes through a forbidden state (red path on the picture below).
The first question is: How is it possible? I suppose this is because of the energy-time uncertainty. The annihilation process is instant (at least looks like on Feynman diagram) and the energy of the intermediate state is not determined. Is it correct?
If we can go through any forbidden state, why doesn't the annihilation go the blue path? This is the second question.
And the third question: Why do electron-hole pairs in semiconductors always emit photons with energy equal to the band gap? Is it just because the interaction with one photon has higher probability or there is a fundamental difference?