"), the sum over all ... states for an ... -subshell of hydrogen-like orbitals reduces to a spherically symmetrical function: ... . For a pure Coulomb potential with any nuclear charge ... , the different ... states for a given ... are also degenerate. The author has derived a generalization of Unsöld's theorem, an explicit form for the sum over both ... and ... for hydrogenic orbitals, namely, ... , where ... is a Whittaker function that can alternatively be written as ... . We can define a radial distribution function (RDF) for a completely filled ... -shell by ... . This is normalized according to ... , reflecting the orbital degeneracy of the energy level ... . In this Demonstration the function ... is plotted for selected values of ... (1 to 10) and ... (1 to 25). L. S. Bartell has derived the classical analog of ... , which, in accordance with Bohr's correspondence principle, approaches the quantum result in the limit ... . The checkbox produces a red plot of the classical function. The generalized Unsöld theorem has found several theoretical applications, including derivation of the canonical Coulomb partition function, density-functional computations, supersymmetry, and study of high- ... Rydberg states of atoms.


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