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

Analytical evaluation of the numerical coefficients in the Zassenhaus product formula and its applications to quantum and statistical mechanics