# How does a system consisting of two nuclei have rotational symmetry?

I don't see it. Can someone explain? The Wikipedia article (http://en.wikipedia.org/wiki/Rotational_symmetry) defines an object with rotational symmetry as an object that looks the same after a certain amount of rotation. But this seems vacuous; doesn't *everything* look the same after a 360$^\circ$ rotation?

Doc Al
Mentor
Keep reading; especially the section titled "n-fold rotational symmetry".

Keep reading; especially the section titled "n-fold rotational symmetry".
I still don't see it. If the nuclei are distinct (say, oxygen and hydrogen), and they are initially at (0,1) and (0,-1), respectively, then only rotation through 360$^\circ$ will leave the system unchanged. If the nuclei are not distinct, however, then I see how rotation through 180$^\circ$ will leave the system unchanged. But I'm not assuming that the nuclei are identical.

Doc Al
Mentor
OK, then I don't get your point. Where does it claim that such a system has anything other than trivial rotational symmetry (except about its central axis, of course)?

OK, then I don't get your point. Where does it claim that such a system has anything other than trivial rotational symmetry (except about its central axis, of course)?
Sorry; maybe I should be more specific. I'm reading a paper, and the argument is made that, because of the "rotational symmetry" of a diatomic molecule, the energy levels of the electrons depend only on the magnitude of the distance between the two nuclei. Does the fact that the system is invariant under 360-degree rotation mean it has rotational symmetry? If so, why should that be sufficient for us to conclude that the electron energy levels are only dependent on the distance between the nuclei and not their orientation?

Doc Al
Mentor
I'm reading a paper, and the argument is made that, because of the "rotational symmetry" of a diatomic molecule, the energy levels of the electrons depend only on the magnitude of the distance between the two nuclei.
The rotational symmetry referred to is with respect to the central axis (the line between the two nuclei).