ABSTRACT

It is convenient to consider the products Cj*Ci as forming a matrix representation of an operator P, with matrix elements 〈 〉i P j C Cj i= ∗ . Substitution for Cj*Ci in Equation 18.1 gives

〈 〉 〈 〉〈 〉 〈 〉A i P j j A i i PA i PA AP

= = = =∑ ∑ ,

( ) ( ).Tr Tr

(18.2)

Tr denotes the diagonal sum of the matrix elements. Equations 18.1 and 18.2 serve as our starting point for the introduction of the density matrix operator.