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

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

Abstract

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.

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