  Relation between Bopp-Kubo formulation and Weyl-Wigner-Moyal symbol calculus,
and non-commutative geometry interpretation of the phase space representation
of quantum mechanics are studied. Harmonic oscillator in phase space via
creation and annihilation operators, both the usual and $q$-deformed, is
investigated. We found that the Bopp-Kubo formulation is just non-commuting
coordinates representation of the symbol calculus. The Wigner operator for the
$q$-deformed harmonic oscillator is shown to be proportional to the 3-axis
spherical angular momentum operator of the algebra $su_{q}(2)$. The relation of
the Fock space for the harmonic oscillator and double Hilbert space of the
Gelfand-Naimark-Segal construction is established. The quantum extension of the
classical ergodiicity condition is proposed.
