Quaternionic differential operators

Motivated by a quaternionic formulation of quantum mechanics, we discuss qu aternionic and complex linear differential equations. We touch only a few a spects of the mathematical theory, namely the resolution of the second orde r differential equations with constant coefficients. We overcome the proble ms coming out from the loss of the fundamental theorem of the algebra for q uaternions 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 the presence of quaternionic potentials, represents an interesting application of the mathe matical material discussed in this paper. (C) 2001 American Institute of Ph ysics.