Solution of the Scalar Coulomb Bethe-Salpeter Equation
High Energy Physics - Theory
2007-05-23 v2 Atomic Physics
Abstract
A relativistic two-body wave equation, local in configuration space, is derived from the Bethe-Salpeter equation for two scalar particles bound by a scalar Coulomb interaction. The two-body bound-state wave equation is solved analytically, giving a two-body Bohr-Sommerfeld formula whose energies agree with the Bethe-Salpeter equation to order alpha^4 for all quantum states. From the Bohr-Sommerfeld formula, along with the expectation values of two remaining small corrections, the energy levels of the scalar Coulomb Bethe-Salpeter equation are worked out to order alpha^6 for all states.
Keywords
Cite
@article{arxiv.hep-th/0006082,
title = {Solution of the Scalar Coulomb Bethe-Salpeter Equation},
author = {John H. Connell},
journal= {arXiv preprint arXiv:hep-th/0006082},
year = {2007}
}
Comments
Revised title, text and alpha^6 results. 21 pages, REVTeX 3