Scattering of a Klein-Gordon particle by a smooth barrier

Abstract

We present the study of the one-dimensional Klein-Gordon equation by a smooth barrier. The scattering solutions are given in terms of the Whittaker $M_{\kappa ,\mu }(x)$ function. The reflection and transmission coefficients are calculated in terms of the energy, the height and the smoothness of the potential barrier. For any value of the smoothness parameter we observed transmission resonances.

arXiv comment14 pages, 7 figures. Accepted in Can. J. Phys

References in corpus (10)

• Scattering of a Klein-Gordon particle by a Woods-Saxon potential
• Bound states of the Klein-Gordon equation in the presence of short-range potentials
• Scattering of a relativistic scalar particle by a cusp potential
• Exact solution of inverse-square-root potential $V\left(r\right)=-\frac{\alpha }{\sqrt{r}}$
• Resonant states in an attractive one dimensional cusp potential
• Proper treatment of scalar and vector exponential potentials in the Klein-Gordon equation: Scattering and bound states
• Scattering solutions of the Klein Gordon equation for a step potential with hyperbolic tangent potential
• Study of superradiance in the Lambert-W potential barrier
• Scattering of a scalar relativistic particle by the hyperbolic tangent potential
• Klein-Gordon equations with homogeneous time-dependent electric fields