The canonical Kravchuk basis for discrete quantum mechanics

The well known Kravchuk formalism of the harmonic oscillator obtained from the direct discretization method is shown to be a new way of formulating di screte quantum phase space. it is shown that the Kravchuk oscillator Hamilt onian has a well defined unitary canonical partner which we identify with t he quantum phase of the Kravchuk oscillator. The generalized discrete Wigne r function formalism based on the action and angle variables is applied to the Kravchuk oscillator and its continuous limit is examined.