Quantum Atom on Valence State

A natural basic test for the just obtained systematic absolute x, tl, IP, and EA density functionals applies for the atomic systems. 

The starting point will be a hydrogenie atom containing an atomic nucleus of charge Z and an electron interacting by means of the Coulomb potential (in atomic units)  

Since the interaction (4.304) is central, the associate wave equation may be separated in spherical polar coordinates to produce the normalized radial function. For the bound states hydrogenic atoms in the case of an infinitely heavy nucleus it looks like (Bransden Joachain, 1983)  

At this point worth noting that, for a given n, there is only one maximum when the quantum orbital number takes its largest value  

Quantum Nanochemistry—Volume II Quantum Atoms and Periodicity 

---