The one-dimensional spinless relativistic Coulomb problem

Motivated by a recent analysis that presents explicitly the general solutio n, we consider the eigenvalue problem of the spinless Salpeter equation wit h a ("hard-core amended") Coulomb interaction potential in one dimension. W e prove the existence of a critical coupling constant (which contradicts th e assertions of the previous analysis) and give analytic upper bounds on th e energy eigenvalues. These upper bounds seem to disprove the previous expl icit solution. (C) 2000 American Institute of Physics. [S0022-2488(00)04004 -4].