On the development of exponential ansatze for quantum dynamics in finite dimensional vector spaces

Abstract

A Wei-Norman type of exponential ansatz is constructed for the time evolution operator in finite dimensional vector spaces. Based on an analysis of the structure of the concerned operator algebra, it is shown that a reduction principle exists even for simple algebras that goes beyond the Wei-Norman result when a specific ordering of the operators is used such that the equations of motion for different generators belonging to different classes are decoupled. It is shown that the solution in this case is global. Some specific approximation schemes are considered and their strengths and weaknesses are analyzed. Model calculations are presented to bring out these features.