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I am reading a book on atom interaction with light. It starts with the 2 level system. The book said the diagonal elements of dipole operator is zero, i.e. ##\langle g|x|g\rangle = \langle e|x|e\rangle = 0##. I don't understand why this is true but after searching online and there gives two reasons

1) the atom has no permanent dipole

2) the symmetry

I read the following post:

https://www.physicsforums.com/threa...s-of-electric-dipole-element-are-zero.706659/

It explains the second reason. But is it always true that any atom will have such symmetry? or does it require the atom is in gas state?If so, why is that?

Also, why ##\langle g|x|g\rangle = \langle e|x|e\rangle = 0## implies no permanent dipole.

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# About diagonal element of dipole

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