Schwartz's method and Goldstein's eigenvalue problem

Abstract

The author uses Schwartz's method to study a relativistic problem whose mathematical structure is similar to Goldstein's eigenvalue problem, i.e. the problem of a zero energy Klein-Gordon particle in an external Coulomb field. It is shown that Schwartz's method fails to give a correct answer. The result suggests that additional information about the eigenvalue spectrum for energies different from zero is needed before deciding whether Goldstein's cut-off independent solution discussed recently by Delbourgo and Prasad is physically meaningful.