Nonrelativistic Limit of a Bethe-Salpeter Equation

Abstract

A two-parameter integral representation for the Bethe-Salpeter amplitude describing a bound state of two scalar particles bound together by scalar mesons is defined. The "ladder approximation" of the Bethe-Salpeter equation is equivalent to an integral equation for the weight function of this representation. In the nonrelativistic limit of infinitely heavy bound particles and zero binding energy, a set of eigenvalues of this equation becomes identical with the spectrum of the corresponding Schrödinger equation with a Yukawa potential.