Interaction and chaotic dynamics of the classical hydrogen atom in an electromagnetic field

TL;DR

This paper derives formulas for energy and angular momentum changes in a classical hydrogen atom interacting with an electromagnetic field, linking energy change to quantum transition matrix elements during specific electron motions.

Contribution

It introduces a new analytical approach connecting classical energy changes with quantum dipole matrix elements during electron motion in a Coulomb field.

Findings

Energy change during electron motion relates to quantum dipole matrix elements.

Expressions derived for energy and angular momentum variations due to electromagnetic interaction.

Focus on energy change between pericenter passages in the classical hydrogen atom.

Abstract

Expressions for energy and angular momentum changes of the hydrogen atom due to interaction with the electromagnetic field during the period of the electron motion in the Coulomb field are derived. It is shown that only the energy change for the motion between two subsequent passings of the pericenter is related to the quasiclassical dipole matrix element for transitions between excited states.