The Radial Functions for the Hydrogenic Atom

Abstract

Because we have solved the angular part of the one-body problem for a spherically symmetric V(r) (or, equivalently, the angular part for the relative motion of a two-body problem), it would be good to provide a detailed example for a particular potential, V(r). Because the Coulomb problem is soluble via the factorization method, let us solve the radial problem for the general hydrogenic atom, i.e., the one electron atom (with Z = 1, 2, 3, ⋯) for hydrogen, once-ionized Helium, twice-ionized Lithium, and so on, where

$$ V(r) = - \frac{{Z{e^2}}}{r} $$

((1))

.