  n-symplectic geometry, a generalization of symplectic geometry on the
cotangent bundle of a manifold M, is formulated on the bundle of linear frames
LM using the Rn-valued soldering 1-form as the generalized n-symplectic
potential. In this paper we use n-symplectic geometry on LRn to formulate a
quantization scheme for a single particle moving in Rn. By retaining the
essence of the standard axioms for quantization on T*Rn, but adapting them to
LR^n, we show it is possible to construct a full polynomial quantization that
is consistent with the Schr\"odinger representation on a 2n-dimensional
subbundle of LRn.
