For indistinguishable particles, the wave function of them should be symmetric or antisymmetric, but in the real world, this might require that all the same type of particles should be considered when solving a specific problem, so I am trying to figure out when could I treat two particles as distinguishable. If the wave function of two particles is not overlapped, it would make sense to treat them as distinguishable, but what if they are overlapped not totally, only partially, would they be distinguishable?


1 Answer 1


If the single-particle wavefunctions of two particles overlap they might be indistinguishable or they might be distinguishable. For two indistinguishable fundamental particles (emergent particles might be more complicated: anyons or nonabelions) we should have Bose or Fermi statistics:

$$\psi(x_1,x_2) = \psi_1(x_1) \psi_2(x_2) \pm \psi_2(x_1) \psi_1(x_2).$$

But the problem is that just looking at the single-particle wavefunctions $\psi_1, \psi_2$ won't tell you this. Also, even if your two particles really did obey the above relation, I don't see any way to rule out the possibility that they were entangled distinguishable particles that just happened to be in a state with Bose or Fermi statistics.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.