Radial functions and total wavefunctions of the hydrogen atom

3 Radial functions and total wavefunctions of the hydrogen atom 

The remaining equation to be solved is the radial equation [eq. (2.1.14)], bearing in mind thatisnowf (f+1) [eq. (2.1.17)]. Hence the solution f (r) also depends on l. In addition, the principal quantum number n arises from the solution of this equation. Thus the radial functions depend on both n and t, and we write them as Rn,i(r). Specifically, n and l take the values 

as energy E appears only in the radial equation, it might be expected to be dependent on n and l and independent of mg. As it turns out, it only depends on n. 

The explicit forms of the radial functions of hydrogenic orbitals Is through 4f are listed in Table 2.1.3, where Z is the nuclear charge of the atom and ao is the Bohr radius  

Note that the radial functions Rn i also form an orthonormal set of functions  

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