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Spin and Orbital Angular Momentum

  1. Nov 18, 2012 #1
    1. The problem statement, all variables and given/known data

    We have a system of 2 indistinguishable spin-1 bosons. We shall adopt the center of mass frame.

    Let
    S = total spin
    L = relative orbital angular momentum
    J = L+S = total angular momentum

    Prove that J = 2m where m is an integer.
    If given that J=1, what are the permissible (L,S) pairs?



    2. Relevant equations
    Bose-Einstein Stats?


    3. The attempt at a solution
    I am lost with this. I have managed to show that for the states S=0, S=2 interchanging particles 1,2 is symmetric, whereas it is antisymmetric for S=1. However, I don't know how to use this here.
    What is the significance of the CoM frame choice?
    Also, due to Bose-Einstein stats, the overall wavefunction should be symmetric under the interchange of the 2 bosons. However, I don't know how even and odd wavefunctions for orbital angular momentum behave. Anyone please?
     
    Last edited: Nov 18, 2012
  2. jcsd
  3. Nov 19, 2012 #2
    No worries. Problem resolved. Thanks for reading anyways.
     
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