Dirac equation: the stationary and dynamical scattering problems

TL;DR

This paper proves that for the radial Dirac equation with Coulomb potential, the dynamical and stationary scattering operators are equivalent, linking quantum scattering theory with classical ergodic results.

Contribution

It establishes the equivalence of dynamical and stationary scattering operators for the radial Dirac equation with Coulomb potential, a novel quantum-classical analogy.

Findings

Dynamical and stationary scattering operators coincide for the radial Dirac equation.

The result provides a quantum analogue of classical ergodic theorems.

The proof connects quantum scattering with classical ergodic behavior.

Abstract

We prove that for the radial Dirac equation with Coulomb-type potential the generalized dynamical scattering operator coincides with the corresponding generalized stationary scattering operator. This fact is a quantum mechanical analogue of ergodic results in the classical mechanics.