Density Matrix Theory and Applications pp 115-163 | Cite as

# Irreducible Components of the Density Matrix

## Abstract

As discussed in Chaps. 1 and 2 it is often useful to expand ρ in terms of a conveniently chosen operator set *Q*_{ i }. This method has two main advantages. First of all, it gives a more satisfactory definition of ρ (see, for example, Sect. 1.1.7), and secondly by using explicitly the algebraic properties of the basis operators the caculations are often greatly simplified (see Sect. 2.5). The usefulness of this method depends on the choice of the basis operator set. When the angular symmetries of the ensemble of interest are important it is convenient to expand ρ in terms of irreducible tensor operators. This method provides a well-developed and efficient way of using the inherent symmetry of the system. It also enables the consequences of angular momentum conservation to be simply allowed for and enables dynamical and geometrical factors in the equation of interest to be separated from each other.