The One-Dimensional Spinless Relativistic Coulomb Problem

Abstract

Motivated by a recent analysis which presents explicitly the general solution, we consider the eigenvalue problem of the spinless Salpeter equation with a ("hard-core amended") Coulomb potential in one dimension. We prove the existence of a critical coupling constant (which contradicts the assertions of the previous analysis) and give analytic upper bounds on the energy eigenvalues. These upper bounds seem to disprove the previous explicit solution.

LaTeX, 11 pages

References in corpus (2)

• Semirelativistic Treatment of Bound States
• Analytical solution of the relativistic Coulomb problem with a hard core interaction for a one-dimensional spinless Salpeter equation

Cited by in corpus (7)

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• Discrete Spectra of Semirelativistic Hamiltonians
• Exact Solutions of Bethe-Salpeter Equations with Instantaneous Interactions
• Stability in the instantaneous Bethe-Salpeter formalism: harmonic-oscillator reduced Salpeter equation
• A new representation for non--local operators and path integrals
• The Spinless Relativistic Kink-Like Problem
• The Spinless Relativistic Hellmann Problem