Scattering of a scalar relativistic particle by the hyperbolic tangent potential

We solve the Klein-Gordon equation in the presence of the hyperbolic tangent potential. The scattering solutions are derived in terms of hypergeometric functions. The reflection, R, and transmission, T, coefficients are calculated in terms of gamma function and, superradiance is discussed, when the reflection coefficient, R, is greater than one. PACS Nos.: 02.30.Gp, 03.65.Pm, 03.65.Nk. Nous solutionnons l'equation de Klein-Gordon en presence d'un potentiel tangent hyperbolique. Les solutions de diffusion sont ecrites a l'aide de fonctions hypergeometriques. Nous calculons les coefficients de reflexion R et de transmission T en termes de fonctions gamma et nous discutons de super-radiance, lorsque le coefficient R est plus grand que un.
1. Introduction The solution of the Klein-Gordon equation with different potentials has been extensively studied in recent years, for bound states and scattering solutions [1-7]. The scattering solutions to the [...]