Why using the word electron for both a free particle and a part of an atom? 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.
 A: I don't really agree with anna v's answer. There is special magic to multiparticle systems in quantum mechanics, namely entanglement, which means that you can't really think of the system as made of independent particles for some purposes. But there's no special magic to bound states. They follow the same rules as unbound states. The laws of physics don't really "know" what a bound state is.
An atom can usefully be treated as a single quantum particle for many purposes, but it's also just a bound state of nucleons and electrons. The nucleons and electrons are still there whether you treat them collectively as an atom or not.
When an atom absorbs a photon and ends up in an excited state, the photon ceases to exist. In electron capture, the electron ceases to exist. When a free proton and electron combine into hydrogen, the electron and proton don't cease to exist. Hydrogen is just an electron and a proton interacting electromagnetically, following the same physical laws they would follow if they were unbound and interacting from a distance.
A: 
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.

We only do this because, due to the large difference in masses of electron vs nucleus, we can approximately treat the atomic nucleus as fixed, and electrons as moving in the nuclear electric field. If we instead had electrons replaced with e.g. muons (which are ~200 times heavier than electrons), we'd no longer have this opportunity, and would have to always talk about excitation of the whole atoms instead of simply atomic electrons.
Even in more complicated systems like molecules, crystals etc. we can use the large difference in nuclear vs electronic masses to devise the Born-Oppenheimer approximation, where nuclei can move, but their motion is effectively separated from the motion of electrons, thus simplifying analysis of the many-particle system in question.
