  Conventional approach to quantum mechanics in phase space, (q,p), is to take
the operator based quantum mechanics of Schrodinger, or and equivalent, and
assign a c-number function in phase space to it. We propose to begin with a
higher level of abstraction, in which the independence and the symmetric role
of q and p is maintained throughout, and at once arrive at phase space state
functions. Upon reduction to the q- or p-space the proposed formalism gives the
conventional quantum mechanics, however, with a definite rule for ordering of
factors of non commuting observables. Further conceptual and practical merits
of the formalism are demonstrated throughout the text.
