  This paper studies the exponential of the sum of two non-commuting operators
as an infinite product of exponential operators involving repeated commutators
of increasing order. It will be shown how to determine two coefficients in
front of the nested commutators in the Zassenhaus formula. The knowledge of one
coefficient is enough to generate a closed formula that has several
applications in solving problems ranging from linear differential equations,
quantum mechanics to non-linear differential equations.
