Wigner function dynamics with boundaries expressed as convolution

In the present paper a method of finding dynamics Wigner function particle in an infinite quantum well is developed. Starting with problem reflection from impenetrable wall, obtained solution then generalized to case confined arbitrary dimensions. It known, that boundary value problems phase space formulation mechanics are surprisingly tricky. The complications arise nonlocality expression involved calculation function. Several ways treating such were proposed. They rather complicated and even exotic, involving, for example, corrections kinetic energy proportional derivatives Dirac delta--function. presented manuscript approach simpler both analytical point view regarding numerical calculation. brought form convolution free some function, defined by shape well. This procedure requires integral, which can be done developed methods.