High-order expansion of the energy eigenvalues of a relativistic Coulomb equation
type: Item
instance of: scholarly article
title: High-order expansion of the energy eigenvalues of a relativistic Coulomb equation
zbMATH Open document ID: 0830.35142
author: Yanyan Li
published in: Annals of Physics
publication date: 1996-01-28T00:00:00Z
full work available at URL: http://cds.cern.ch/record/258054
review text: It is shown that the Herbst equation, i.e., a Coulomb potential wave equation including a free relativistic kinetic energy, presents a rather nontrivial series expansions of its eigenvalues in powers of \(\alpha\). In fact, in contrast to Klein-Gordon and Dirac equations, it presents not only odd powers of \(\alpha\) but also nonanalytic \(\ln \alpha\) terms. The first orders \((\alpha^4, \alpha^5)\) are obtainable by a standard perturbation method on the Sommerfeld correction. A much more effective and systematic method is proposed to get higher orders \((\alpha^7)\). To appreciate the resulting expansion, we compare it to the known results coming from other approaches to relativistic bound states, namely Klein- Gordon and Dirac equations in an external field and for the two-body problem, the Breit and Sucher-type equations, and the positronium QED result.
Mathematics Subject Classification ID: 35Q75
Mathematics Subject Classification ID: 81Q05
Mathematics Subject Classification ID: 35P05
zbMATH DE Number: 788132
zbMATH Keywords: series expansion of eigenvalues
zbMATH Keywords: Herbst equation
zbMATH Keywords: Sommerfeld correction
zbMATH Keywords: relativistic bound states
zbMATH Keywords: Breit and Sucher-type equations
MaRDI profile type: Publication
OpenAlex ID: W2080629028
DOI: 10.1006/APHY.1995.1034
description: scientific article; zbMATH DE number 788132