Inspired by a recently proposed procedure by Leonhardt and Raymer for wavepacket reconstruction, we calculate the irregular wavefunctions for the bound states of the Coulomb potential. We select the irregular solutions which have the simplest semiclassical limit.
We study the Hydrogen atom as a quantum mechanical system with a Coulomb like potential, with a semiclassical approach based on an effective description of quantum mechanics. This treatment allows us to describe the quantum state of the system as a system of infinite many classical equations for expectation values of configuration variables, their moments and quantum dispersions. It also provides a semiclassical description of the orbits and the evolution of observables and spreadings and their back-reaction on the evolution.