In classical mechanics, the position
and momentum
of some component of a dynamical system are represented as *real numbers* which,
by definition, commute.
In quantum mechanics, these quantities are represented
as *non-commuting* linear Hermitian operators acting in a ket space
that represents all of the possible states of the system. Our first task is
to discover a quantum mechanical replacement for the classical result
.

Richard Fitzpatrick 2013-04-08