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The most common isotope of hydrogen has no neutrons. Other isotopes are deuterium with 1 neutron and tritium, with 2 neutrons. Since virtually all (99.98% according to wiki) naturally occurring hydrogen comes in the no neutron isotope, it seems reasonable that books show a schematic of that one when illustrating hydrogen. As a secondary motivation, the one ...


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The chemical properties of an element are always determined by the atomic number, that is, the number of protons in the nucleus. All carbon atoms have six protons, all iron atoms have 26, etc. It's the atomic number which is featured prominently in the periodic table, for example. Until the neutron was discovered in 1932, this was fine. After the neutron ...


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The relativistic generalization of the formula; and the replacement of the electron mass by the reduced mass are clearly two basically independent steps (at least in the leading approximation), and both of them have to be applied to agree with the experiment. The most accurate experimental value of the energy is $-13.59844\,{\rm eV}$, see NIST: ...


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It is all over the place, but it's involved. It is normally calculated from the path integral propagator. The most concise source of the radial Green's function you are after is eqn (15) of Grosche 1998, in terms of modified Bessel functions, integral rep, $$ G_l^C(r'',r';E) = \int_0^\infty\dfrac{e^{i e^2s''/\hbar}ds''}{\sqrt{v'v''}} ...



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