  We discuss the variety of coordinates often used to characterize the coherent
state classical limit of an algebraic model. We show selection of appropriate
coordinates naturally motivates a procedure to generate a single particle
Schr\"odinger hamiltonian which, for low energy states, gives equivalent
results to a bosonic algebraic model to leading order in $N$. The process is
used to study the associated geometries of the dynamical symmetries of U(3). By
demanding that the inner product be preserved in the Schr\"odinger picture we
conclude that different dynamical symmetries correspond to different scales.
