In the present paper we discuss a possibility to construct both a probabilistic representation and a probabilistic approximation of the Cauchy problem solution for an equation $\frac{\partial u}{\partial t}=\frac{\sigma^2}{2}\,\Delta u+V(x)u,$ where $\sigma$ is a complex parameter such that $\mathrm{Re}\,\sigma^2\geqslant 0$. This equation coincides with the heat equation when $\mathrm{Im}\,\sigma=0$ and with the Schr\"odinger equation when $\sigma^2=iS$ where $S$ is a positive number.