Using classical probabilistic methods we construct a probabilistic approximation in $L_2$ of the Cauchy problem solution for an equation $\frac{\partial u}{\partial t}=\frac{\sigma^2}{2}\,\Delta u+V(x)u,$ where $\mathrm{Re}\,V\leqslant 0$ and $\sigma$ is a complex parameter with $\mathrm{Re}\,\sigma^2\geqslant 0$. This equation coincides with the heat equation when $\mathrm{Im}\,\sigma=0$ and with the Schr\"odinger equation when $\mathrm{Re}\,\sigma^2=0$.