  Many quantization schemes rely on analogs of classical mechanics where the
connections with classical mechanics are indirect. In this work I propose a new
and direct connection between classical mechanics and quantum mechanics where
the quantum mechanical propagator is derived from a variational principle. I
identify this variational principle as a generalized form of Hamilton's
principle. This proposed variational principle is unusual because the physical
system is allowed to have imperfect information, i.e., there is incomplete
knowledge of the physical state. Two distribution functionals over possible
generalized momentum paths a[p(t)] and generalized coordinates paths b[q(t)]
are defined. A generalized action is defined that corresponds to a contraction
of a[p(t)], b[q(t)], and a matrix of the action evaluated at all possible p and
q paths. Hamilton's principle is the extremization of the generalized action
over all possible distributions. The normalization of the two distributions
allows their values to be negative and they are shown to be the real and
imaginary parts of the complex amplitude. The amplitude in the Feynman path
integral is shown to be an optimal vector that extremizes the generalized
action. This formulation is also shown to be directly applicable to statistical
mechanics and I show how irreversible behavior and the micro-canonical ensemble
follows immediately.
