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Annals of Physics

Explicit solution of the continuous Baker-Campbell-Hausdorff problem and a new expression for the phase operator

I. Bialynicki-Birula

Published Dec 1, 1968• 12 citations
Publisher
DOI
10.1016/0003-4916(68)90135-8

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Explicit solution of the continuous Baker-Campbell-Hausdorff problem and a new expression for the phase operator

Iwo Białynicki‐Birula, Bogdan Mielnik, Jerzy F Plebanski

Annals of Physics•Jan 1, 1969•148 citations

Error bounds for the truncated Baker--Campbell--Hausdorff and Zassenhaus formulas in unitary problems

A. Arnal, F. Casas, J. L. Ruiz-Benito

The Baker--Campbell--Hausdorff (BCH) formula plays a critical role in many branches of mathematics and physics. It expresses the logarithm of the product of exponentials of non-commuting operators as an infinite series of nested commutators of the operators involved. The Zassenhaus formula is the dual of the BCH formula: the exponential of a sum of operators is written as an infinite product of exponentials involving the operators and their commutators. In practical computations, however, one typically has to truncate the expansions, and so understanding the error committed by the resulting approximations and eventually providing suitable bounds for this error is of paramount interest. In this work we present a general strategy to derive rigorous error bounds and explicit error constants for the BCH and Zassenhaus formulas when the operators involved are skew-adjoint, as is the case for quantum evolution problems.

math-phCross-listedarXiv:2607.07692•Jul 9, 2026

On Baker-Campbell-Hausdorff operator disentangling by similarity transformations

Wolfgang Witschel

Physics Letters A•Oct 1, 1985•17 citations

The Phase-Amplitude representation of a wave function revisited

George H. Rawitscher

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A generalization of the phase approach to scattering theory, and some numerical results

Francesco Calogero, D. G. Ravenhall

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Solution of the Schr�dinger Equation for a Linear Potential using the Extended Baker-Campbell-Hausdorff Formula

Francisco Soto, H. M. Moya-Cessa

The time-dependent Schr¨ odinger equation is solved for a linear potential using operational methods ; in particular, an extension of the Baker-Campbell-Hausdorff formula is exposed and used. Several initial conditions are considered. A closed form for the Wigner function is presented. The results can be extended to the propagation of an electromagnetic field in the paraxial approximation. odinger equation, linear potential, Zassenhaus formula, Baker-Campbell-Hausdorff formula, Wigner function

Applied Mathematics & Information Sciences•Sep 8, 2014•10 citations
The Baker--Campbell--Hausdorff (BCH) formula plays a critical role in many branches of mathematics and physics. It expresses the logarithm of the product of exponentials of non-commuting operators as an infinite series of nested commutators of the operators involved. The Zassenhaus formula is the dual of the BCH formula: the exponential of a sum of operators is written as an infinite product of exponentials involving the operators and their commutators. In practical computations, however, one typically has to truncate the expansions, and so understanding the error committed by the resulting approximations and eventually providing suitable bounds for this error is of paramount interest. In this work we present a general strategy to derive rigorous error bounds and explicit error constants for the BCH and Zassenhaus formulas when the operators involved are skew-adjoint, as is the case for quantum evolution problems.