  In this paper we present a direct perturbative method to solving certain
Fokker-Planck equations, which have constant diffusion coefficients and some
small parameters in the drift coefficients. The method makes use of the
connection between the Fokker-Planck and Schr\"odinger equations. Two examples
are used to illustrate the method. In the first example the drift coefficient
depends only on time but not on space. In the second example we consider the
Uhlenbeck-Ornstein process with a small drift coefficient. These examples show
that the such perturbative approach can be a useful tool to obtain approximate
solutions of Fokker-Planck equations with constant diffusion coefficients.
