Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Formula di Baker-Campbell-Hausdorff e ampiezze di transizione

Pietro Oreglia

Published Dec 1, 2017• 0 citations
OpenAlex

Abstract

The idea is to study the Baker-Campbell-Hausdorff formula and its recent developments to highlight its behavior. Then we use that formula to calculate the propagator in quantum mechanics if the system considered is a harmonic oscillator.

Related papers

Functional forms for the squeeze and the time-displacement operators

Michael Martin Nieto

Using Baker - Campbell - Hausdorff relations, the squeeze and harmonic-oscillator time-displacement operators are given in the form , where , , and are explicitly determined. The applications are discussed.

arXiv:quant-ph/9605032•Quantum and Semiclassical Optics Journal of the European Optical Society Part B•Oct 1, 1996•20 citations

The harmonic oscillator propagator

Barry R. Holstein

The Feynman propagator for the harmonic oscillator is evaluated by a variety of path-integral-based means.

American Journal of Physics•Jul 1, 1998•58 citations

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

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

An elementary derivation of the oscillator propagator

L. Moriconi

American Journal of Physics•Jan 1, 2004•0 citations

Baker-Campbell-Hausdorff formulae and spherical and hyperbolic rotations

M. A. M. Santiago

Using Baker-Campbell-Hausdorff formulae for the exponentials of the generators of the SU 2 and SU(1,1) groups, the matrix elements of spherical and hyperbolic rotations are calculated in the angular momentum basis.

Journal of Physics A Mathematical and General•Jun 1, 1976•15 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.