Typical states and density matrices

It is shown how, for an n-dimensional Hilbert space, one may translate the density matrix formalism into a sort of classical probability theory on the space of quantum states, P_n-1 ( C). Because of the intricate blend of complex, Riemannian and symplectic geometry which arises from the Kähler structure on this manifold, under this transcription Schrödinger's equation becomes Hamilton's equation and Heisenberg's equation becomes Liouvillc's equation. The formalism suggests some natural generalizations of conventional quantum mechanics which are briefly described.