Eigenvalues of the Breit Equation

Abstract

Eigenvalues of the Breit Equation {eqnarray*} [(\vecα_{1} \vec{p} + β_{1}m)_{αα^{\prime}} δ_{ββ^{\prime}} + δ_{αα^{\prime}} (-\vecα_{2} \vec{p} + β_{2}M)_{ββ^{\prime}} - \frac{e^{2}}{r} δ_{αα^{\prime}} δ_{ββ^{\prime}}] Ψ_{α^{\prime} β^{\prime}} = E Ψ_{αβ}, {eqnarray*} in which only the static Coulomb potential is considered, have been found. Here the detailed discussion on the simple caces, ${}^1{S}_0,m=M$ and $m\ne M$ is given deriving the exact energy eigenvalues. The ${\alpha }^2$ expansion is used to find radial wave functions. The leading term is given by classical Coulomb wave function. The technique used here can be applied to other cases.

14 pages, no figure