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Is dipole operator symmetric or antisimmetric? Or, in other words, do the transition dipole moments from state 1 to the state 2, and from the state 2 to the state 1 have different sign? I.e.

mu_12 = - mu_21.

As far as I understand, the diagonal elements for the dipole operator should be zero (since the transition dipole moments from state "n" to the same state "n" should ne zero). However, in this case the dipole moments of all excited states should be zeros! This does not look to be physical. How one can resolve this contradiction?

Thank you in advance.

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# Dipole moment operator.

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