  The effect of Kolmogorov-Arnold-Moser (KAM) theorem in quantum systems is
manifested in dividing eigenstates into regular and irregular states. We
propose an effective method based on Wannier basis in phase space to illustrate
this division of eigenstates. The quantum kicked-rotor model is used to
illustrate this method, which allows us to define the area and effective
dimension of each eigenstate to distinguish quantitatively regular and
irregular eigenstates. This Wannier basis method also allows us to define the
length of a Planck cell in the spectrum that measures how many Planck cells the
system will traverse if it starts at the given Planck cell. Moreover, with this
Wannier approach, we are able to clarify the distinction between KAM effect and
Anderson localization.
