  Motivated by a quaternionic formulation of quantum mechanics, we discuss
quaternionic and complex linear differential equations. We touch only a few
aspects of the mathematical theory, namely the resolution of the second order
differential equations with constant coefficients. We overcome the problems
coming out from the loss of the fundamental theorem of the algebra for
quaternions and propose a practical method to solve quaternionic and complex
linear second order differential equations with constant coefficients. The
resolution of the complex linear Schrodinger equation, in presence of
quaternionic potentials, represents an interesting application of the
mathematical material discussed in this paper.
