Comment on ‘Special-case closed form of the Baker–Campbell–Hausdorff formula’

Recently Van-Brunt and Visser (2015 J. Phys. A: Math. Theor. 48 225207) succeeded in explicitly evaluating the Baker–Campbell–Hausdorff (BCH) expansion series for the noncommuting operators X and Y, provided that the two operators satisfy the commutation relation: , and the operator I commutes with both of them. In this comment we show that the closed-form BCH formula of this special case can be straightforwardly derived by the means of the Wei–Norman theorem and no summation of the infinite series is needed.