As for classical dynamics, a stroboscopic point of view can be adopted by introducing the time propagator over a kicking period U ^ ^ (that is the Floquet operator) so that | ψ ψ ( t + T ) ⟩ ⟩ = U ^ ^ | ψ ψ ( t ) ⟩ ⟩ . After a careful integration of the time-dependent Schrödinger's equation, one finds that U ^ ^ can be written as the product of two operators U ^ ^ = exp ⁡ ⁡ [ − − i p ^ ^ 2 T 2 I ℏ ℏ ] exp ⁡ ⁡ [ − − i K T ℏ ℏ cos ⁡ ⁡ θ θ ^ ^ ] We recover the classical interpretation: the dynamics of the quantum kicked rotor between two kicks is the succession of a free propagation during a time T followed by a short kick. This simple expression of the Floquet operator U ^ ^ (a product of two operators, one diagonal in momentum basis, the other one diagonal in angular position basis) allows to easily numerically solve the evolution of a given wave function using split-step method.