Radial eigenfunctions table

The pre-exponential factors in the equation 1.12 normalize the Slater approximations to the radial components of atomic orbitals. Normality is not an inherent property of linear combinations of Slater orbitals, for example, as in Table 1.3, and it is important to check any published coefficients to determine whether normalization is included. In addition, the Slater orbitals for a set of atomic orbitals in an atom are not mutually orthogonal. The results of atomic structure calculations using Slater orbitals, either as single functions or in linear combinations, as in double-zeta sets, of course, are mutually orthogonal, since this property of the eigenfunctions, is mirrored in the final linear combinations returned by the calculations for the eigenvalues. 

The Slater function for the 1 s orbital in hydrogen is the exact eigenfunction of Table 1.1. So the first significant calculation involves the Slater 2s radial function. From equation 1.12,... 

Table 17.2 Radial Factors for Hydrogen-Like Energy Eigenfunctions...

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