- #1
hendriko373
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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?
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
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