Consider a system of two identical particles. The combined system of these two particles has a total orbital angular momentum quantum number $\ell = 1$.
I am aware that the spatial wavefunction of a system with $\ell = 1$ has odd parity, as this can be shown from the spherical harmonics. However, I am not sure if anything can be said about the exchange symmetry of the spatial wavefunction in this case.
I.e. is the spatial wavefunction of the combined system symmetric or antisymmetric under exchange of the particle labels? And could you explain why.