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According to various other answers on this site, most seem to feel that the Bohr Radius is the most accurate size of the hydrogen atom assuming this is defined as the radius where the electron is most often. This would seem to be contradicted by https://en.wikipedia.org/wiki/Bohr_radius which includes a section on reduced mass effects. So which is correct, the Bohr Radius or the version with reduced mass?

Derek Seabrooke
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    The correction is small and therefore often ignored. There are also other corrections. – Ghoster Dec 10 '22 at 05:23
  • Do you have the complete calculation? – Derek Seabrooke Dec 10 '22 at 05:25
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    I don’t think it can be exactly calculated because all the higher-order quantum-field-theoretic effects are so complicated. But I think I’ve seen a calculation using the Dirac wavefunction. This would include relativistic effects and spin effects, but not things like vacuum polarization by virtual electron-positron pairs. – Ghoster Dec 10 '22 at 05:26
  • @Ghoster this is very interesting. – Derek Seabrooke Dec 10 '22 at 05:30
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    Yes. A century after quantum mechanics, I know of no truly exact solution even for “simple old hydrogen” taking all QFT effects into account, even one treating the proton as elementary. However, we can probably do theoretical calculations that are at least as accurate as experimental measurements. – Ghoster Dec 10 '22 at 05:32
  • @Ghoster this is quite shocking. Has none attempted it? – Derek Seabrooke Dec 10 '22 at 05:36
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    I’m sure people have tried. Some quantum field theories are exactly solvable, but QED is apparently not one of them. Fortunately, perturbation theory seems to work well for getting accurate-but-approximate results that agree with experiments. – Ghoster Dec 10 '22 at 05:39
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    For helium and other atoms, we don’t even have an exact solution of the Schrodinger equation! But this doesn’t stop physicists from understanding atomic structure quite well. – Ghoster Dec 10 '22 at 05:52

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