Double bar matrix element

  1. malawi_glenn

    malawi_glenn 4,726
    Science Advisor
    Homework Helper

    Is wondering if anyone knows if the modulus square of the double matrix element that arises in Wigner-Eckart theorem obeys the same "rule" as the ordinary does, if the operator is hermitian:

    [tex] |<ajm|M|bj'm'>|^2 = |<bj'm'|M|ajm>|^2 [/tex] if M is hermitian.

    Is then :

    [tex] |<aj||M||bj'>|^2 = |<bj'||M||aj>|^2 [/tex] ?

    ---

    I think it does, the Wigner-Eckart theorem states:

    [tex] \langle njm|T^k_q|n'j'm'\rangle =\langle nj||T_q||n'j'\rangle C^{jm}_{kqj'm'} [/tex]

    where [tex] C^{jm}_{kqj}[/tex] is a Clebsh gordan


    So I think things will work out, are someone sure about how these things work, please tell me :)
     
  2. jcsd
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