  Defining the observable ${\bf \phi}$ canonically conjugate to the number
observable ${\bf N}$ has long been an open problem in quantum theory. Here we
show how to define the absolute phase observable ${\bf \Phi}\equiv |{\bf\phi}|$
by suitably restricting the Hilbert space of $x$ and $p$ like variables. This
${\bf \Phi}$ is actually the absolute value of the phase and has the correct
classical limit. A correction to the ``cosine'' ${\bf C}$ and ``sine'' ${\bf
S}$ operators of Carruthers and Nieto is obtained.
