# Identical Particle Wavefunctions

Consider the process $$\rho^0\rightarrow\pi^0+\pi^0$$ The $\rho^0$ has $J=1$ whilst the two pions have $S_{tot}=0$ and thus require $L_{tot}=1$ by conservation of angular momentum. Consequently this process is forbidden because the pions are identical bosons and must have a wavefunction that is symmetric under particle exchange and $L_{tot}=1$ does not allow this.

I am happy with this but for the last sentence. Could somebody go into how the collective orbital angular momentum of a system of two particles relates to the symmetry of the two particle wavefunction under exchange of particles? Thank you for any help :)

This is due to the property of the angular part of the wave function, namely the spherical harmonics. When you have a parity transform (inversion through the origin), spherical harmonics transform like this: $$Y_{lm}(\theta, \phi) \rightarrow (-1)^l Y_{lm}(\theta, \phi)$$