The quantum dynamics of a Gaussian wavepacket in the quantum phase spa
ce of the driven surface state electron (SSE) Hamiltonian is studied.
Using the Husimi phase space representation of quantum mechanics we de
monstrate that the prominent KAM island persists in the quantum domain
as the dynamical barrier which prevents the wavepacket from exploring
the classically inaccessible regions. The structure of classical phas
e space is clearly manifested in the properties of the Floquet states
dominating the dynamics of the wavepacket.