  We provide geometric quantization of the vertical cotangent bundle V^*Q
equipped with the canonical Poisson structure. This is a momentum phase space
of non-relativistic mechanics with the configuration bundle Q -> R. The goal is
the Schrodinger representation of V^*Q. We show that this quantization is
equivalent to the fibrewise quantization of symplectic fibres of V^*Q -> R,
that makes the quantum algebra of non-relativistic mechanics an instantwise
algebra. Quantization of the classical evolution equation defines a connection
on this instantwise algebra, which provides quantum evolution in
non-relativistic mechanics as a parallel transport along time.
