 Floquet's theorem guarantees that the solutions to an equation of this form can be written as

formula_13

Here, formula_14 is the "bare" energy for no coupling to the electromagnetic field, and formula_15 has the same time-periodicity as the Hamiltonian,

formula_16

or

formula_17

with formula_18 the angular frequency of the field.Because of its periodicity, it is often further useful to expand formula_19 in a Fourier series, obtaining

or

formula_21

where formula_22 is the frequency of the laser field.The solution for the joint particle-field system is therefore a linear combination of stationary states of energy formula_23, which is known as a "quasi-energy" state and the new set of energies are called the "spectrum of quasi-harmonics".