Hydrogen atom in the phase-space formulation of quantum mechanics

Using a coordinate transformation which regularizes the classical Kepler problem, we show that the hydrogen-atom case may be analytically solved via the phase-space formulation of nonrelativistic quantum mechanics. The problem is essentially reduced to that of a four-dimensional oscillator whose treatment in the phase-space formulation is developed. Furthermore, the method allows us to calculate the Green's function for the H atom in a surprisingly simple way.