Is it possible to have identical quantum particles that are distinguishable? By identical, I only mean that all particle properties like mass, spin, charge, etc., are identical. My guess would be no because the only thing that could tell the two apart is their trajectories, but their wavefunctions may overlap, which in my mind ought to make them indistinguishable. Is that anywhere in the ballpark of the right way to think about it? On the other hand, is it theoretically possible to make gaseous atoms, as would normally obey the Maxwell-Boltzmann distribution, instead behave like a Fermi-Dirac or Bose-Einstein gas under the right conditions and on the right energy scales? Is there a well-known example of this? Would the superfluid phase transition of liquid helium be a valid instance?