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When I see depictions of the electron orbital of a hydrogen atom, I see a static proton in the center surrounded by an electron cloud. What would it look like if we shifted the reference frame to the electron and observed the proton? That is, what would it look like if we assumed the electron was statically positioned in the center and the proton formed a cloud around it? It seems arbitrary to me that we should choose the proton as the center of reference save only that it has more mass.

If anyone knows where I could look to see depictions of such a frame of reference shift, or is able to model one, I would be grateful.

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  • $\begingroup$ This is often done to explain spin-orbit coupling: the orbiting positive charge is a current loop acting on the electron spin. $\endgroup$ – user137289 Oct 7 '20 at 23:38
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    $\begingroup$ Although you can’t see the difference, the depictions are not in the proton’s frame but in the center-of-mass frame, which is an inertial frame. Neither the proton’s frame nor the electron’s frame is inertial. $\endgroup$ – G. Smith Oct 7 '20 at 23:58
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The quantity which is statistically distributed is the vector between the electron and the proton. That remains the same regardless of how we fix our reference frame.

Thus, if we fix the electron static at (0, 0, 0) and let the proton move, the resulting shape is exactly the opposite of what we get with the proton static at (0, 0, 0) and letting the electron move. And, as most orbitals are symmetric, we would not observe any meaningful change in what it looks like. The visual image would be identical.

Of course, the fixed nucleus does have one huge advantage over the electron: most nuclei are extended, meaning they take up a 3d dimensional space. This means we can talk about orientation of the coordinate system with respect to the protons and neutrons. In the case of an electron, it's a point or a spherically symmetric shape, depending on how you want to think about it. There is no meaningful orientation for an electron, so you would have to come up with an orientation from somewhere else (such as the orientation of a test apparatus).

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