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](adsbygoogle = window.adsbygoogle || []).push({});

>On the other hand, two [itex]π^0[/itex]’s cannot be in an [itex]l = 1[/itex] 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 [itex]l = 1[/itex] state is antisymmetric if we interchange the two pions. This means that the decay mode [tex]\rho^0\to \pi^0+\pi^0[/tex] is forbidden.

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

Thanks.

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# Why the antisymmetry?

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