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Wigner-Eckart theorem and selection rules

  1. Oct 15, 2006 #1
    If you have an operator which in spherical tensor language

    [tex]
    T^k_q
    [/tex]

    are

    [tex]
    V=T^2_2 + T^2_{-2} + T^2_0
    [/tex]

    you get a selection rule for j'

    [tex]
    abs(j-k)=< j' <= j+k
    [/tex]

    in my case i start with angular momentum j=1 and k=2 from above so
    the possible new states are

    [tex]
    1=< j' <= 3
    [/tex]

    But the operator is even under parity and the angular momentum states have parity (-1)^j=-1 in my case.
    What does this mean for the possible states j=1 can jump to?

    from the selection rule above you get that

    j=1 to j'=2
    j=1 to j'=3

    is possible but does the parity consideration remove any of these possibilities?
     
    Last edited: Oct 15, 2006
  2. jcsd
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