  We present a Feynman-Kac formula for the $1$-dimensional stochastic heat
equation (SHE) driven by a time-homogeneous Gaussian white noise potential,
where the noise is interpreted in the Wick-It\^o-Skorokhod sense.
  Our approach consists in constructing a Wong-Zakai-type approximation for the
SHE from which we are able to obtain an "approximating Feynman-Kac"
representation via the reduction of the approximated SHE to a deterministic
partial differential equation (PDE). Then we will show that those
"approximating Feynman-Kac" converge to a well defined object we will call
"formal Feynman-Kac" representation which happens to coincide with the unique
solution of SHE.
