Proof of Moszkowski's Formula for the Variance of Term Energies in an Electronic Configuration of the Formln

Abstract

The formula in question is ${\sigma }^2\left(E \mathrm{in} l^n\right)=\left[\frac{n(n-1\mathrm{})\mathrm{}(4l+2-n)\mathrm{}(4l+2-n-1)\mathrm{}}{2\left(4l\right)\mathrm{}(4l-1)\mathrm{}}\right]{\sigma }^2\left(E \mathrm{in} l^2\right).\mathrm{}$ The proof makes use of probability matrices rather than of fractional parentage coefficients.