Solutions to the 1d Klein–Gordon equation with cut-off Coulomb potentials

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Abstract In a recent paper by Barton [G. Barton, J. Phys. A: Math. Gen. 40 (2007) 1011], 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 Letter, these results are completely confirmed by a numerical formulation that also allows a solution for an alternative cut-off Coulomb potential V 2 ( | x | ) = − α / | x | , | x | > a , and otherwise V 2 ( | x | ) = − α / a .