  We give a simple demonstration that the Schr\"odinger equation may be recast
as a self-contained second-order Newtonian law for a congruence of spacetime
trajectories. This provides a pictorial representation of the quantum state as
the displacement function of the collective whereby quantum evolution is
represented as the deterministic unfolding of a continuous coordinate
transformation. Introducing gauge potentials for the density and current
density it is shown that the wave-mechanical and trajectory pictures are
connected by a canonical transformation. The canonical trajectory theory is
shown to provide an alternative basis for the quantum operator calculus and the
issue of the observability of the quantum state is examined within this
context. The construction illuminates some of the problems involved in
connecting the quantum and classical descriptions.
