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[itex]^\circ[/itex] will leave the system unchanged. If the nuclei are not distinct, however, then I see how rotation through 180[itex]^\circ[/itex] will leave the system unchanged. But I'm not assuming that the nuclei are identical.Doc Al said:Keep reading; especially the section titled "n-fold rotational symmetry".
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 said: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)?
The rotational symmetry referred to is with respect to the central axis (the line between the two nuclei).AxiomOfChoice said: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.
Rotational symmetry in a system consisting of two nuclei refers to the property of the system remaining the same after being rotated around its center. This means that the system will have the same physical properties, such as shape and orientation, regardless of the angle of rotation.
Rotational symmetry in a system consisting of two nuclei is achieved when the forces between the nuclei are evenly distributed, resulting in a balanced system. This allows the system to maintain its shape and orientation, even when rotated.
Rotational symmetry is important in a system consisting of two nuclei because it allows for the system to have stable and predictable behavior. The symmetry ensures that the system maintains its properties and does not undergo any drastic changes due to rotation.
Rotational symmetry can affect the energy levels in a system consisting of two nuclei by allowing for degeneracy, or equal energy levels, to occur. This is because the symmetry allows for different orientations of the system to have the same energy, resulting in degenerate energy levels.
Yes, rotational symmetry can be broken in a system consisting of two nuclei if the forces between the nuclei are not evenly distributed. This can result in an imbalance in the system, causing it to become unstable and potentially leading to changes in its properties when rotated.