For the composite system of identical particles only symmetric and antisymmetric states in the tensor-product (from the one-particle spaces) space are allowed to represent particles in nature. Why is that?(adsbygoogle = window.adsbygoogle || []).push({});

Is it an experimental fact which is used as an input in the theory of many particle QM?

Or

Is it a consequence of the commutation relation [tex]\left[P,Q\right]=0[/tex] with P the permutation operator and Q an observable (this commution relation is just the mathematical formulation for the indistinguishability of our many particle system)? This would conclude that P and Q have a common eigenbasis (but which space would span this basis?) whereas the eigenvectors from P are (anti)symmetric so that the action of Q on the system also puts the system in a (anti)symmetric state?

thanks in advance,

Hendrik

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# Symmetric/Antisymmetric states in nature?

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