Effective Hamiltonian Theory from a Quantum Method of Averaging

We provide a useful method of deriving the time-averaged Hamiltonian of a quantum system that includes non-harmonic perturbations and naturally preserves hermiticity to the desired order of approximation. This is achieved using a Quantum Method of Averaging formalism that, in addition to extending the periodic/harmonic perturbation requirement of prior effective theories, provides a simple convergence requirement, presents a validity condition at each order, and bounds the approximation errors. We will demonstrate the capabilities of the method using examples relevant to the AMO community.