This questions stems from Anna's answer here: https://physics.stackexchange.com/a/578929/230132
Quoting her, she says an electron bound to a nucleus is not a quantum entity, the entire atom is. And she adds that as such the two are not separable.
My knowledge of QM is rudimentary, but I think I understand what she means.
However it makes me wonder why we keep talking of electrons when they are bound to a nucleus if they are not separable, if only for logical reasons and semantic reasons.
When a photon sets an electron to a higher energy level, we stop talking of the photon: we act as if the photon vanished and its energy was now in the electron.
Same with electron capture: the final product is not generally considered to contain an electron.
So why in the case of an atom there still are electrons and not some excited state or whatever of the atom?
I assume this is merely an arbitrary choice to simplify discussions about the atom's state and a vestige of the past. But if someone has a better answer, please help.