Symmetric Expansion of One- and Two-Center Coulomb Potentials

Abstract

A one‐center expansion of the electrostatic interaction energy of a discrete charge distribution is developed by making use of the algebra of irreducible tensors. The result is completely symmetric in the coordinates of the particles, and the relative magnitude of the vectors need not be specified. It is shown that a suitable interaction representation provides useful formulas for electrostatic and quantum mechanical applications. In addition, some transformation equations make it possible to refer any arbitrary number of vectors to a second origin, thus yielding general two‐center expansions for overlapping charge distributions.