An operational perspective on the Magnus–Fer conundrum in time-dependent quantum mechanics

The development of analytic methods for studying quantum systems driven by periodic Hamiltonians has remained an active pursuit for gaining insights into physical phenomena in spectroscopy and other related areas in chemical physics. From a theoretical perspective, the success of a given analytic method relies on the operational aspects as well as its exactness in replicating (known) experimental results. While analytic methods built around the Magnus expansion (ME) scheme have been preferred in time-evolution studies, the splitting of the time-propagator into a product of exponential operators in the Fer expansion (FE) scheme has gained wider attention in recent years. To this end, the operational advantages of one scheme over the other have always remained contentious and form the basis for the present report. Employing periodic Hamiltonians as examples, the operational aspects and the relative merits/demerits of the two methods are analyzed, and their long-term/short-term behavior is discussed through analytic expressions in experimentally verifiable systems.