Quantum coherent states are key in the quantum-classical correspondence: the expectation values of positions and momenta of wave packets defined as coherent states behave according to the classical dynamics; i.e. the expectation values follow the classical trajectories. Heisenberg calculated explicitly coherent states for the simple harmonic oscillator. More recently, coherent states for the hydrogen atom have been studied.

We analyze how the procedure can be generalized to periodically driven quantum systems. The dynamics of the hydrogen atom in a microwave field is studied in terms of quantum Floquet states. We propose a combination of Floquet states to form wave packets that are well localized in the classical three-dimensional configuration space. These wave packets feature the properties of quantum coherent states: they have a recurrence time, collapses and revivals.

Furthermore, we analyze the classical phase space structure by means of wavelet based frequency analysis. With this methodology, we show that both regular and chaotic behavior appear. The coherent states can be located in regions of the phase space where regular dynamics occurs due to resonance with the driving field.