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Why the antisymmetry?

  1. Dec 10, 2012 #1
    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 [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.
     
    Last edited by a moderator: May 6, 2017
  2. jcsd
  3. Dec 10, 2012 #2

    Bill_K

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    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.
     
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