Comment on ``A simple expression for the terms in the Baker-Campbell-Hausdorff series''

TL;DR

This paper critically examines Reinsch's matrix method for the Baker-Campbell-Hausdorff series, demonstrating that it offers no computational advantage over straightforward series expansion.

Contribution

It clarifies the equivalence of Reinsch's matrix approach to direct series expansion, challenging claims of efficiency improvements.

Findings

Reinsch's matrix method is equivalent to straightforward series expansion.

The method does not reduce computational effort.

No efficiency gain over traditional series expansion.

Abstract

It is pointed out that Reinsch's matrix operation formulation of calculating the Baker-Campbell-Hausdorff series [math-ph/9905012] is equivalent to the straightforward series expansion. The amount of calculation does not decrease by his method.