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i'm studying the paragraph 5.5 (page 119) of this book:

http://sciold.ui.ac.ir/~sjalali/MSc.Students/statistical.mechanics/pathria.pdf

Now at page 121 we have:

$$ \sum\limits_{p} \delta_p{u_{k1}}(P1) \cdot... \cdot u_{kN}(PN) \sum\limits_{P'} \delta_{P'} u^*_{P'k_1}(1') \cdot ... \cdot u^*_{P'k_N} (N') $$

Now he says that since a permutation among the $k_i$ changes the wave function at most by a sign we can sobstitute the second summation with a $N!$. I don't understand this fact. Why is the permutation irrelevant and add only a $N!$?

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  • $\begingroup$ Minor comment to the post (v2): Please consider to mention explicitly author, title, etc. of link, so it is possible to reconstruct link in case of link rot. $\endgroup$ – Qmechanic Nov 26 '18 at 15:30

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