Scattering of a scalar relativistic particle by the hyperbolic tangent potential

Abstract

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.

6 pages, 3 figures. arXiv admin note: substantial text overlap with arXiv:1409.5787

References in corpus (6)

• History and Physics of the Klein Paradox
• 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
• Scattering and Bound State Solutions of Asymmetric Hulthén Potential
• Bound states of scalar particles in the presence of a short range potential

Cited by in corpus (3)

• Relativistic time-dependent quantum dynamics across supercritical barriers for Klein-Gordon and Dirac particles
• Klein paradox for bosons, wave packets and negative tunnelling times
• Scattering of a Klein-Gordon particle by a smooth barrier