  Without wasting time and effort on philosophical justifications and
implications, we write down the conditions for the Hamiltonian of a quantum
system for rendering it mathematically equivalent to a deterministic system.
These are the equations to be considered. Special attention is given to the
notion of 'locality'. Various examples are worked out, followed by a systematic
procedure to generate classical evolution laws and quantum Hamiltonians that
are exactly equivalent. What is new here is that we consider interactions,
keeping them as general as we can. The quantum systems found, form a dense set
if we limit ourselves to sufficiently low energy states. The class is discrete,
just because the set of deterministic models containing a finite number of
classical states, is discrete. In contrast with earlier suspicions, the
gravitational force turns out not to be needed for this; it suffices that the
classical system act at a time scale much smaller than the inverse of the
maximum scattering energies considered.
