  Based on the Koopman-van Hove (KvH) formulation of classical mechanics
introduced in Part I, we formulate a Hamiltonian model for hybrid
quantum-classical systems. This is obtained by writing the KvH wave equation
for two classical particles and applying canonical quantization to one of them.
We illustrate several geometric properties of the model regarding the
associated quantum, classical, and hybrid densities. After presenting the
quantum-classical Madelung transform, the joint quantum-classical distribution
is shown to arise as a momentum map for a unitary action naturally induced from
the van Hove representation on the hybrid Hilbert space. While the quantum
density matrix is positive by construction, no such result is currently
available for the classical density. However, here we present a class of hybrid
Hamiltonians whose flow preserves the sign of the classical density. Finally,
we provide a simple closure model based on momentum map structures.
