# 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

## Answers and Replies

Physics Monkey
Science Advisor
Homework Helper
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.

Try it in one dimension to get a feeling for things.

Hope this helps.

Yes that makes sense, thank you. If we had a system of say 3 protons the the overall angular momentum would not tell us about the symmetry with respect to particle exchange - is that correct?