  In this paper we provide the DeWitt propagator and its wave function in
quantum cosmology using the path integral formulation of quantum gravity. The
DeWitt boundary condition is introduced as a way to avoid the Big Bang
singularity by positing that the wave function of the universe vanishes near
the Big Bang. However, there is currently no clear definition of the DeWitt
boundary condition in the path integral formulation. To address this issue, we
use the image method, which eliminates singular paths in the forbidden region
of the infinite potential, and apply this method to quantum cosmology based on
the Batalin-Fradkin-Vilkovisky formulation of the path integral. We investigate
the validity of the image method, and in particular, find that this method is
only appropriate when the potential has symmetry with respect to the boundary.
We then show that the DeWitt propagator and the DeWitt wave function derived
from the image method are consistent with solutions of the Wheeler-DeWitt
equation for certain models of quantum cosmology.
