  We examine the quantization of pseudoclassical dynamical systems, models that
have classically anticommuting variables, in the Schr\"odinger picture. We
quantize these systems, which can be viewed as classical models of particle
spin, using the generalized Gupta-Bleuler method as well as the reduced phase
space method in even dimensions. With minimal modifications, the standard
constructions of Schr\"odinger quantum mechanics of constrained systems work
for pseudoclassical systems. We generalize the standard Schr\"odinger norm and
implement the correct adjointness properties of observables and constraints. We
construct the state space corresponding to spinors as physical wave functions
of anticommuting variables, finding that there are superselection sectors in
both the physical and ghost subspaces. The physical states are isomorphic to
those of the Dirac-K\"ahler formulation of fermions though the inner product in
Dirac-K\"ahler theory is not equivalent to ours.
