Solutions to the 1d Klein-Gordon equation with cutoff Coulomb potentials

Abstract

In a recent paper by Barton (J. Phys. A40, 1011 (2007)), the 1-dimensional Klein-Gordon equation was solved analytically for the non-singular Coulomb-like potential V_1(|x|) = -α/(|x|+a). In the present paper, these results are completely confirmed by a numerical formulation that also allows a solution for an alternative cutoff Coulomb potential V_2(|x|) = -α/|x|, ~|x| > a, and otherwise V_2(|x|) = -α/a.

arXiv comment8 pages, 4 figures

References in corpus (1)

• The hydrino and other unlikely states

Cited by in corpus (8)

• Approximate Analytical Solutions to Relativistic and Nonrelativistic Pöschl-Teller Potential with its Thermodynamic Properties
• The Klein-Gordon equation with the Kratzer potential in d dimensions
• Effective-Mass Klein-Gordon-Yukawa Problem for Bound and Scattering States
• Special comparison theorem for the Dirac equation
• Comparison theorems for the Klein-Gordon equation in d dimensions
• Mathematical predominance of Dirichlet condition for the one-dimensional Coulomb potential
• Sharp comparison theorems for the Klein--Gordon equation in $d$ dimensions
• Some new solutions to the Klein-Gordon equation in 1-1D space-time in the presence of time dependent potentials