ABSTRACT
In this chapter, the authors focus on the range of utility of the most popular parametrizations of the time-evolution operator that they study by means of the Lie algebraic method. The solution to the Schrodinger equation with an acceptable model Hamiltonian exists for all physically relevant values of time. There has been great interest in the convergence properties of the Magnus, because its failure seems to be the origin of some conflicting results. An example is the wrong long-time behavior of spectroscopic properties obtained from the average Hamiltonian theory, which is based on the first term of the Magnus expansion. The other most popular parametrization of the time-evolution operator is a product of exponentials that has been known for a long time to exhibit some advantages with respect to the single exponential or Magnus form. The authors investigate the range of utility of a fully factorized time-evolution operator by means of simple models based on finite-dimensional Lie algebras.
