# Are all identical fermions in orthogonal states as opposed to different general states?

A professor told me that most physicists assume that all identical fermions are in completely orthogonal states. If that is true, then does that mean that that the total wave function is highly localized for a closed box of a huge number of electrons? I get confused between when your supposed multiply wavefunctions and when your supposed to add wavefunctions. I know that for one electron, adding all orthogonal states of that one electron in a closed box would yield a highly localized spatial wavefunction.

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Orthogonal states in what space? "All fermions" in the sense of "all electrons" or in the sense of "the electron, the muon, the up quark..."? Why would orthogonality of states imply high localization (momentum eigenstates are also orthogonal and highly non-localized, for example)? More information, please! –  ACuriousMind Jul 17 at 18:21
I think your professor might have said or meant completely antisymmetric N-particle states. As to the second question, the answer is no, you do not simply add the single-particle wavefunctions. Your N-particle wavefunction is a function of the form $\Psi(x_1,x_2,...,x_N)$ and it can't be generally written as a product of single-particle wavefunctions. –  Void Jul 17 at 18:55
Is there a way to add observables? –  linuxfreebird Jul 17 at 18:57