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The orbits of planets have some ellipticity. Is there any corresponding ellipticity in the orbital of electrons?

Are we able to see some ellipticity at least for a many electron atom, if not for the Hydrogen like atoms? I expect to see some ellipticity.

We solve the Hydrogen atom problem invoking the reduced mass that is equivalent to reducing the problem from the one of two bodies to the one of single body (the electron). How/what will be the solution if we solve the H-atom problem as a two body problem, that is, what will be the orbital for the nucleus as well as that of the electron that we get as the result?

Are we able to see some ellipticity at least for a many electron atom, if not for the Hydrogen like atoms? I expect to see some ellipticity.

We solve the Hydrogen atom problem invoking the reduced mass that is equivalent to reducing the problem from the one of two bodies to the one of single body (the electron). How/what will be the solution if we solve the H-atom problem as a two body problem, that is, what will be the orbital for the nucleus as well as that of the electron that we get as the result?

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