2018/04/03 by Mauro Bologna, Bologna, Mauro
Computer Science · Mathematics · Physics and Astronomy · #Matrix Theory and Algorithms #Spectral Theory in Mathematical Physics #advanced mathematical theories #cond-mat.stat-mech
paper · pdf · doi:10.48550/arxiv.1804.01125
18 pages, 4 figures
arxiv created 2018/04/03 · arxiv updated 2018/04/05
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.