We have here a two-body problem, of an electron of charge -e and mass m, and a proton of charge +e and mass M. By using CM and relative coordinates and working in the CM frame, we can reduce the problem to the dynamics of a single particle whose mass µ = mM /(m + M) is the reduced mass and whose coordinate r is the relative coordinate of the two particles. However, since m/M ≃ 1/2000, as a result of which the relative coordinate is essentially the electron's coordinate and the reduced mass is essentially m, let us first solve the problem in the limit M→∞. In this case we have just the electron moving in the field of the immobile proton. At a later stage, when we compare the theory with experiment, we will see how we can easily take into account the finiteness of the proton mass.
KeywordsHydrogen Atom Recursion Relation Outer Shell Nuclear Charge Schrodinger Equation
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