Why are fermion-only or boson-only systems easier to study than mixed states?

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Tio Barnabe
In general, is it of more interest to consider multi particle states consisting of fermions & bosons or multi particle states consisting of only fermions (or only bosons)? I have seen that if it's of the latter type, then the study becomes in certain way more easy to carry on, though the former seems to be more general.
 
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If you're considering spontaneous emission from excited atoms, you have to include both electrons (fermions) and photons (bosons) in the model. Same applies when studying electron-phonon interaction in condensed matter physics.
 
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