Can identical particles be distinguishable?

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Twigg
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Main Question or Discussion Point

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?
 

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Is it possible to have identical quantum particles that are distinguishable?
No, by definition of "identical" and quantum mechanics.
but their wavefunctions may overlap
You cannot consider single-particle wave functions any more, you have to take a single wave function to describe both, and there is no "first particle here, second here" any more.
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?
It is impossible to avoid this. FD and BE are the more fundamental distributions, for large temperatures they both can get approximated by Maxwell-Boltzmann.
 
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Twigg
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Makes sense. Thanks!
 

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