  In this paper, we propose a complex approach to evaluate a function sum of
two noncommuting non Hermitian operators. Then, it is proposed an explicit
expansion of the evolution operator in the case of the neutral K-meson system
under the influence of an external interaction. Then, the importance of the
procedure is pointed out to consider the algebraic expansion of the time
evolution operator whenever the dynamics decouples the internal transitions and
the center of mass motion.
