Scattering of a Klein-Gordon particle by a Hulth\'en potential

TL;DR

This paper provides an exact analytical solution to the Klein-Gordon equation with a Hulthén potential, analyzing scattering states, transmission coefficients, and resonance conditions in a one-dimensional quantum system.

Contribution

It presents an exact solution for the Klein-Gordon equation with a Hulthén potential and investigates transmission resonances and their dependence on potential shape.

Findings

Transmission coefficients derived analytically

Conditions for transmission resonances identified

Zero-reflection condition depends on potential shape

Abstract

The Klein-Gordon equation in the presence of a spatially one-dimensional Hulth\'en potential is solved exactly and the scattering solutions are obtained in terms of hypergeometric functions. The transmission coefficient is derived by the matching conditions on the wavefunctions and the condition for the existence of transmission resonances are investigated. It is shown how the zero-reflection condition depends on the shape of the potential.