In my lecture on indistinguishable particles, my lecturer is trying to illustrate to me the notion of particles being indistinguishable when considering that when we swap two particles in a box the superposition state looks absolutely the same. She then goes on to note:

If we consider the phase of the wavefunction, then it turns out that there are two possible outcomes for the overall two-particle wavefunction, which either maintains or reverses its sign every time a swap between particles is made

I don't see how this happens. A global phase shouldn't change the wavefunction appreciably. Can someone explain why what she is saying is the case?

  • $\begingroup$ Phase factors can be signed, + or - and therefore act differently. en.m.wikipedia.org/wiki/Identical_particles $\endgroup$ – StudyStudy Apr 12 at 21:49
  • $\begingroup$ Ask your lecturer what happens to the phase if you use a density matrix model of the two particles. $\endgroup$ – Carl Brannen Apr 13 at 3:26

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