  We present a generally covariant approach to quantum mechanics in which
generalized positions, momenta and time variables are treated as coordinates on
a fundamental "phase-spacetime." We show that this covariant starting point
makes quantization into a purely geometric flatness condition. This makes
quantum mechanics purely geometric, and possibly even topological. Our approach
is especially useful for time-dependent problems and systems subject to
ambiguities in choices of clock or observer. As a byproduct, we give a
derivation and generalization of the Wigner functions of standard quantum
mechanics.
