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What gives us the certainty that the unit charge of a free electron - measured and confirmed with the highest precision in numerous experiments - is retained even when approaching and integrating into an atom and associated with the emission of EM radiation?

Subordinate questions, which should primarily serve to understand the above question: Has a measurement procedure been devised or already carried out that can experimentally investigate the charge or electric field strength of the bound electron? Would such research simplify the model of the fundamental electromagnetic interaction in the atom?

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  • $\begingroup$ "Subordinate questions..." You should spend more time clarifying the first question rather than piling on additional questions. It's not clear if you are trying to ask about some new or non-mainstream physics, or if you are trying to ask about differences in renormalization between free electrons vs bound electrons, or something else... $\endgroup$
    – hft
    Commented Jan 6 at 19:21

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Scattering experiments are sensitive to the charge of the nucleus while bound to an atom. So if we take those as confirming the charge of the nucleus bound to the atom then we can combine measurements of the free electron, the bound nucleus, and the bound atom. When we do that we find that the difference between the charge of the nucleus and the atom is equal to the charge of the free electron.

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  • $\begingroup$ That is beyond any doubt. I just didn't dare to ask the question a little more deeply. Doesn't the proton also lose its charge to the same extent? And does it regain this charge when exposed to the energy that is sufficient to separate the proton and electron again / knock the electron out of the atom? Doesn't the whole story become radically simpler? Even if it never becomes measurable, it should make the calculations of QM easier. $\endgroup$
    – HolgerFiedler
    Commented Jan 7 at 5:32
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Quantum mechanics perfectly explains atoms and molecules. Any significant discrepancy would immediately be raised to the highest attention level. That is enough evidence for me until a counterexample emerges.

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