  Motivated by the work of Baras-Goldstein (1984), we discuss when expectations
of the Feynman-Kac type with singular potentials are divergent. Underlying
processes are Brownian motion and $\alpha$-stable process. In connection with
the work of Ishige-Ishiwata (2012) concerned with the heat equation in the
half-space with a singular potential on the boundary, we also discuss the same
problem in the half-space for the case of Brownian motion.
