# Double bar matrix element

1. Feb 14, 2008

### malawi_glenn

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:

$$|<ajm|M|bj'm'>|^2 = |<bj'm'|M|ajm>|^2$$ if M is hermitian.

Is then :

$$|<aj||M||bj'>|^2 = |<bj'||M||aj>|^2$$ ?

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

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

where $$C^{jm}_{kqj}$$ is a Clebsh gordan

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