# Particle exchange and parity

I'm struggling with the relation between particle exchange and parity with the case of para- and ortho-hydrogen.

The overall wavefunction must be antisymmetric with respect to particle exchange and so for para-hydrogen (an antisymmetric spin state) the spatial part of the wavefunction must be symmetric with respect to particle exchange.

My notes say that because the parity of a state of angular momentum quantum number l is (-1)^l then for para-hydrogen l may only take even values. I'm struggling to see the relationship between parity and particle exchange in this case, can anyone help?

Thanks

Physics Monkey
If $$\vec{r}$$ is the relative position of the two identical particles, then parity $$\vec{r} \rightarrow - \vec{r}$$ is formally like particle exchange. Does that make sense? Thus in simple cases the parity of the wavefunction tells you about the symmetry or antisymmetry under particle exchange.