Fermion occupation (1 Viewer)

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1. The problem statement, all variables and given/known data prove , using appropriate commutation relations that the number operator yields the values 0 and 1 for fermions , and any non - negative values for bosons.



2. Relevant equations the commutation relations for bosons and fermions.



3. The attempt at a solutionthe boson case is solved.
the fermions-i can understand this thing intuitively ,because on applying the number operator on a state containing n fermions in a single state , and then using commutation relation i am getting (-n) as eigenvalue which is absurd. but i do not know how to give a more compact proof.
 
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The problem is not precisely stated. The number operator for fermions can as well have eigenvalue 100 - can't you have 100 of electrons? Of course you can. Probably what you mean is the number of fermions in a given state. In that case you indeed use anticommutation relations, but you end up with the eigenstate being equal to its minus, not with the eigenvalue equal to its minus!
 
yes. i meant single state.
i have understood my mistake. thanks.
 

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