  It is studied time dependence of the evolution operator kernel for the
Schr\"odinger equation with a help of the Schwinger -- DeWitt expansion. For
many of potentials this expansion is divergent. But there were established
nontrivial potentials for which the Schwinger -- DeWitt expansion is
convergent. These are, e.g., V=g/x^2, V=-g/cosh^2 x, V=g/sinh^2 x, V=g/sin^2 x.
For all of them the expansion is convergent when $g=\lambda (\lambda -1)/2$ and
$\lambda$ is integer. The theories with these potentials have no divergences
and in this meaning they are "good" potentials contrary to other ones. So, it
seems natural to pay special attention namely to these "good" potentials.
Besides convergence they have other interesting feature: convergence takes
place only for discrete values of the charge $g$. Hence, in the theories of
this class the charge is quantized.
