Parametric time-coherent states for the hydrogen atom

We obtained coherent states for the hydrogen atom by transforming the problem into four oscillators in the parametric time at a classical level, and quantizing these oscillators by using path integration over their holomorphic coordinates. We showed that for the negative- (positive-) energy coherent states the mean values of the physical position of the electron satisfy the Keplerian ellipses (hyperbolas) and that their dispersions oscillate (increase) in parametric time.