Further Developments of Angular-Momentum Graphs. Applications to Physical Problems

Abstract

In this chapter we shall develop the graphical methods of representing angular momentum further by means of a number of theorems, first given by Jucys, Levinson and Vanagas (JLV) [1962]. We shall then use these theorems to derive a general expression for the matrix elements of a tensor-operator product between coupled states in a purely graphical way. Finally, we shall apply these results to an important physical problem—the Coulomb interaction of a twoelectron system—in some detail. This example clearly demonstrates the usefulness of the graphical technique in dealing with angular-momentum problems of certain complexity. In a later chapter (Chap. 8)—after having studied the physical properties of atoms more systematically—we shall extend the technique further and apply it to general many-electron systems.