Classical dynamics with Schrodinger equation What are some interesting classical systems for which the dynamics can be reduced to a many-body Schrodinger equation, at least in some useful regions of phase space, and in particular, with many variables.
 A: Maybe the following is not quite what you want, but there are no other answers so far, so, for what its worth...
In my recent article (Eur. Phys. J. C (2013)73:2371, open access, http://download.springer.com/static/pdf/480/art%253A10.1140%252Fepjc%252Fs10052-013-2371-4.pdf?auth66=1385089451_f596af16d4caeff5e91ad116fca2ad96&ext=.pdf ), I consider two realistic non-second-quantized theories: scalar electrodynamics (Klein-Gordon-Maxwell electrodynamics) and spinor electrodynamics (Dirac-Maxwell electrodynamics). While these theories contain the Planck constant, they are classical (field theories) in the same sense as classical electrodynamics is classical.
I showed that (with some caveats) the matter fields can be algebraically eliminated, so the theories are pretty much equivalent to some systems of PDEs (partial differential equations) for electromagnetic field only, furthermore, they describe independent dynamics of electromagnetic field. It also turns out that these theories can be embedded into quantum field theories, so they are equivalent to some subsets of multi-particle solutions of the quantum field theories.
