We propose a unified approach for different exponential perturbation techniques used in the treatment of time-dependent quantum mechanical problems, namely the Magnus expansion, the Floquet--Magnus expansion for periodic systems, the quantum averaging technique and the Lie--Deprit perturbative algorithms. Even the standard perturbation theory fits in this framework. The approach is based on carrying out an appropriate change of coordinates (or picture) in each case, and can be formulated for any time-dependent linear system of ordinary differential equations. All the procedures (except the standard perturbation theory) lead to approximate solutions preserving by construction unitarity when applied to the time-dependent Schr\"odinger equation.

翻译：我们提出了一种统一方法，用于处理时间相关量子力学问题中使用的不同指数扰动技术，即马格努斯展开、用于周期系统的Floquet–马格努斯展开、量子平均技术以及Lie–Deprit扰动算法。即使标准微扰理论也适用于这一框架。该方法基于在每种情况下进行适当的坐标变换（或表象变换），并可推广至任意时间相关的线性常微分方程组。所有程序（标准微扰理论除外）在应用于含时薛定谔方程时，都能通过构造方式保持幺正性，从而获得近似解。