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 V1(|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 V2(|x|) = -α/|x|, ~|x| > a, and otherwise V2(|x|) = -α/a.
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