For bosons we define states as eg.(adsbygoogle = window.adsbygoogle || []).push({});

ln> = l1 0 1 ... >

where the numbers denote how many particles belong to the j'th orbital.

And similarly for fermions. We then define creation and anihillation operators which raise and lower the number of particles in the j'th orbital:

c_j, c_j^(dagger)

Now in many problems I have to commute bosons and fermion operators. I actually asked this question before, but I didn't completely understand the answer. My question is:

Why does fermion and boson operators commute? starting from the wavefunction symmetrization and antisymmetrization requirement

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# Boson and fermion operators

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