If the wave function of a system of two identical fermions is antisymmetric, how can they be identical? I replace two 'identical' particles and get a different system. This must mean they are not identical. Why isn't this contradictory?
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2$\begingroup$ Does this (or any of the many similar previous questions) answer your question? When are two fermions considered identical? $\endgroup$– RococoDec 22, 2019 at 2:21
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Since the wave function $\psi$ comes back to $-\psi$ under exchange of the particles, the probability density $\vert\psi\vert^2$ does not change and is thus independent of how you label the fermions.
answered Dec 21, 2019 at 18:28