Proper treatment of scalar and vector exponential potentials in the Klein-Gordon equation: Scattering and bound states

Abstract

We point out a misleading treatment in the literature regarding to bound-state solutions for the $s$-wave Klein-Gordon equation with exponential scalar and vector potentials. Following the appropriate procedure for an arbitrary mixing of scalar and vector couplings, we generalize earlier works and present the correct solution to bound states and additionally we address the issue of scattering states. Moreover, we present a new effect related to the polarization of the charge density in the presence of weak short-range exponential scalar and vector potentials.

arXiv comment6 pages

References in corpus (4)

• Dirac and Klein-Gordon equations with equal scalar and vector potentials
• Bound states of the Klein-Gordon equation in the presence of short-range potentials
• Scattering of a relativistic scalar particle by a cusp potential
• Effects of a mixed vector-scalar screened Coulomb potential for spinless particles

Cited by in corpus (4)

• On beautiful analytic structure of the S-matrix
• Scattering of a Klein-Gordon particle by a smooth barrier
• Morse potential in relativistic contexts from generalized momentum operator, Pekeris approximation revisited and mapping
• Uniform magnetic field on the relativistic spinless particles with constant rest mass: 2D polar space