- #1

ChrisVer

Gold Member

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Hey I was reading through a text and came across:

I can understand the second statement from the Pauli matrices... However I think that I don't understand the 1st statement as it is... why would the diagonal elements of an odd-operator be zero if parity is definite?

"[Having extracted the Dirac version of Schrodinger's equation of the H atom...] Since the states [itex] | j j_z l >[/itex] have definite parity, the odd-operator [itex] \vec{S} \cdot \hat{r}[/itex] will have vanishing diagonal elements. Also since [itex]\big(\vec{S} \cdot \hat{r} \big)^2 =1[/itex] then its offdiagonal elements will be [itex] \frac{1}{2} e^{\pm i \phi} [/itex] (we can choose the phase [itex]\phi=0[/itex])[...]"

I can understand the second statement from the Pauli matrices... However I think that I don't understand the 1st statement as it is... why would the diagonal elements of an odd-operator be zero if parity is definite?

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