The phase-space formulation of the nonrelativistic quantum mechanics is constructed on the basis of a deformation of the classical mechanics by the $\ast$-product. We have taken up the MIC-Kepler problem in which Iwai and Uwano have interpreted its wave-function as the cross section of complex line bundle associated with a principal fibre bundle in the conventional operator formalism. We show that its Green's function, which is derived from the $\ast$-exponential corresponds to unitary operator through the Weyl application, is equal to the infinite series that consists of its wave-functions. Finally, we obtain its Wigner function.
"Green's Function, Wavefunction and Wigner Function of the MIC-Kepler Problem." J. Geom. Symmetry Phys. 30 63 - 73, 2013. https://doi.org/10.7546/jgsp-30-2013-63-73