  In this paper we extend Schwinger's quantization approach to the case of a
supermanifold considered as a coset space of the Poincare group by the Lorentz
group. In terms of coordinates parametrizing a supermanifold, quantum mechanics
for a superparticle is constructed. As in models related to the usual
Riemannian manifold, the key role in analyzes is played by Killing vectors. The
main feature of quantum theory on the supermanifold consists of the fact that
the spatial coordinates are not commute with each other and therefore are
represented on wave functions by integral operators.
