A simple proof of Floquet's theorem for the case of unitary evolution in quantum mechanics
@inproceedings{Martin2021ASP, title={A simple proof of Floquet's theorem for the case of unitary evolution in quantum mechanics}, author={J. D. D. Martin and A. N. Poertner}, year={2021} }
where E is a diagonal matrix containing the ǫj ’s, and Φ(t) is periodic; i.e., Φ(t) = Φ(t+ T ) for all t. Despite the relative simplicity of this result, it is not standard quantum mechanics textbook fare (with at least one exception [4]). But due to the fundamental nature of this “time version” of Bloch’s theorem and recent activity in time-periodic quantum-mechanical Floquet systems (see, for example, Ref. [5]), it may be desirable to study it in quantum mechanics courses. The purpose of this…
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