  A formalism is presented in which quantum particle dynamics can be developed
on its own rather than `quantization' of an underlying classical theory. It is
proposed that the unification of probability and dynamics should be considered
as the basic feature of quantum theory. Arguments are given to show that when
such a unification is attempted at the configuration space level, the wave
funtions of Schr$\ddot{o}$dinger theory appear as the natural candidates for
the desired unification. A *-algebra $\mathcal{A}_{Q}$ of (not necessarily
bounded) linear operators acting on an appropriate dense set of these wave
functions appears as the arena for quantum kinematics. A simple generalization
of an existing formalism in noncommutative geometry is employed to develop the
notion of generalized algebraic symplectic structure (GASS) which can
accomodate classical and quantum symplectic structures as special cases.
Quantum kinematics and dynamics is developed in in the framework of a
noncommutative Hamiltonian system employing an appropriate GASS based in $
\mathcal{A}_{Q}$. The Planck constant is introduced at only one place -- in the
quantum symplectic form; its appearance at conventional places is then
automatic. Unitary Wigner symmetries appear as canonical transformations in the
noncommutative Hamiltonian system. A straightforward treatment of quantum -
classical correspondence is given in terms of appropriate GASSes.
