Effective quantum equations for the semiclassical description of the Hydrogen atom

TL;DR

This paper develops an effective semiclassical framework for the hydrogen atom, translating quantum dynamics into classical equations for expectation values and moments, enabling a detailed analysis of quantum effects on classical orbits.

Contribution

It introduces a novel semiclassical approach that models the hydrogen atom using an infinite set of classical equations for quantum expectation values and dispersions.

Findings

Provides a semiclassical description of hydrogen atom orbits.

Captures quantum back-reaction effects on classical trajectories.

Enables analysis of quantum dispersions and their evolution.

Abstract

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.