Introduction to Quantum Physics and Information Processing

The Essentials of Quantum Mechanics 43

3.2.2 Self-adjoint operators

An operator is said to be self-adjoint if it satisfies

hv|

ˆ

A|wi = hv|

ˆ

A

†

|wi. (3.7)

The corresponding matrix is said to be Hermitian. An important conse-

quence of self-adjointness is that the eigenvalues will turn out to be real. A

self-adjoint operator is thus a good candidate for a physical observable whose

values are always real.

Postulate 2. Observables An observable A in quantum mechanics is usually

represented by a self-adjoint operator

4

ˆ

A. Measurement of A in an experiment

gives a real number value α, which is one of the eigenvalues of the operator

ˆ

A.

By “measurement of an observ ...