A pedagogical approach to the Magnus expansion

Abstract

Time-dependent perturbation theory as a tool to compute approximate solutions of the Schrödinger equation does not preserve unitarity. Here we present, in a simple way, how the Magnus expansion (also known as exponential perturbation theory) provides such unitary approximate solutions. The purpose is to illustrate the importance and consequences of such a property. We suggest that the Magnus expansion may be introduced to students in advanced courses of quantum mechanics.