Why the antisymmetry?

1. Dec 10, 2012

c299792458

Would someone please explain the following found on P. 125 of these notes http://www.hep.phys.soton.ac.uk/hepwww/staff/D.Ross/phys3002/PCCP.pdf? [Broken]

>On the other hand, two $π^0$’s cannot be in an $l = 1$ state. The reason for this is that pions are bosons and so the wavefunction for two identical pions must be symmetric under interchange, whereas the wavefunction for an $l = 1$ state is antisymmetric if we interchange the two pions. This means that the decay mode $$\rho^0\to \pi^0+\pi^0$$ is forbidden.

I don't understand why the wavefunction of $l = 1$ must be antisymmetric. Perhaps I have forgotten something?

Thanks.

Last edited by a moderator: May 6, 2017
2. Dec 10, 2012

Bill_K

The spin part is 0 x 0 which is symmetric. And the parity of an orbital wavefunction with angular momentum ℓ is (-), so ℓ = 1 is antisymmetric under interchange of the particles.