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At the moment, the most efficient method to compute the state of aperiodically driven quantum system is using Floquet theory and the Floqueteigenbasis. The wide application of this basis set method is limited by: a lackof unique ordering of the Floquet eigenfunctions, an ambiguity in theirdefinition at resonance, and an instability against infinitesimal perturbationat resonance. We address these problems by redefining the eigenbasis using arevised definition of the average energy as a quantum number. As a result ofthis redefinition, we also obtain a Floquet-Ritz variational principle, andjustify the truncation of the Hilbert space.

Defining a well-ordered Floquet basis by the average energy