  Canonical BRST quantization of the topological particle defined by a Morse
function h is described. Stochastic calculus, using Brownian paths which
implement the WKB method in a new way providing rigorous tunnelling results
even in curved space, is used to give an explicit and simple expression for the
matrix elements of the evolution operator for the BRST Hamiltonian. These
matrix elements lead to a representation of the manifold cohomology in terms of
critical points of h along lines developed by Witten.
