I’m wondering about bosons and anti-symmetric spin states. (Throughout this post I’ll be using symmetric and anti-symmetric with respect to exchange of particle labels.)

It is well known that bosons have symmetric overall wavefunctions while fermions have anti-symmetric overall wavefunctions. For fermions, this overall anti-symmetry can be (and is!) created either by having an anti-symmetric spin wavefunction paired with a symmetric non-spin wavefunction or by a symmetric spin wavefunction paired with an anti-symmetric non-spin wavefunction.

Intuitively, one would suppose that bosons could equally produce a wavefunction with overall symmetry either by having two symmetric components or two anti-symmetric components. I’m currently tutoring a course on quantum mechanics which states without proof that bosons *always* occupy symmetric spin states, and thus need symmetric spatial states to produce an overall symmetry if those are the only degrees of freedom available. I’m perfectly willing to accept this, but I’d like to have something more convincing to tell my students than ‘the book says so’.

I tried to google appropriate terms with no luck and opened the question up to my fellow graduate students at tea, but there is no joy. So I turn to the physics minds of the Straight Dope: assuming that it is true that bosons never occupy antisymmetric spin states, why is this so? Why does the same reasoning not prevent fermions from occupying symmetric spin states?