Scattering of a Klein–Gordon particle by a Hulthén potential

Abstract

The Klein-Gordon equation in the presence of a spatially one-dimensional Hulthén 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.

Scattering and bound state solutions of the asymmetric Hulthén potential

“…The scattering solutions of the Klein-Gordon equation for the general Hulthén potential have been obtained and transmission resonances investigated in Ref. [13]. Guo et.al.…”

Scattering of a spinless particle by an asymmetric Hulthén potential within the effective mass formalism

“…[9]. After these pioneering studies, the transmission resonance and supercriticality for the relativistic/non-relativistic particles in an external potentials have been extensively discussed [3,11,12,13,14,15,16,17,18]. In one of these studies [13], the authors showed that the transmission coefficient obtained for the Klein-Gordon particle displays a behavior similar to that of the one obtained for the Dirac particle [8].…”

Scattering of a scalar relativistic particle by the hyperbolic tangent potential

“…The solution of the Klein-Gordon equation with different potentials has been extensively studied in recent years, for bound states and scattering solutions [1][2][3][4][5][6][7]. The scattering solutions to the Dirac equation also have been studied for several potentials, a particular case is the Hulthén potential [8].…”