Effective quantum equations for the semiclassical description of the   Hydrogen atom
  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. 
Guillermo Chac\'on-Acosta and H\'ector H. Hern\'andez
quant-ph gr-qc