Expectation Values

(58) |

which reduces to

(59) |

with the aid of Equation (54).

Consider the identity operator, 1. All states are eigenstates of this operator with the eigenvalue unity. Thus, the expectation value of this operator is always unity: i.e.,

for all . Note that it is only possible to normalize a given ket , such that Equation (60) is satisfied, because of the more general property (21) of the norm. This property depends on the previously adopted correspondence (16) between the elements of a ket space and those of its dual bra space.