Scattering of scalar relativistic particle by the Lambert-W potential

In this work we derive the Klein-Gordon equation that is a relativistic wave equation. This equation describes all spinless particles with positive, negative as well as zero charge. As a quantized field theory, the Klein-Gordon equation describes bosons. Particularly, we are going to study the scattering solutions of the one-dimensional Klein-Gordon equation with the Lambert-W potential barrier. We also study the scattering solutions of the hyperbolic tangent potential and the step potential. These idealized potentials are studied in this research because they are relatively easy to understand and they are exemplary approximations to real ones. The scattering solutions are derived in terms of hypergeometric functions, and discussed in terms of the height of the potential barrier. We divide our research into three regions, observing superradiance in one of them. At last, we discuss the phenomenon known as Klein Paradox when more particles are reflected by a potential than are incident on it.

• Glavni autor: Puente Lapuerta, Luis Germán (author)
• Format: bachelorThesis
• Jezik: eng
• Izdano: 2019
• Teme: Ecuación de Klein-Gordon; Potencial Lambert-W; Estados de dispersión; Funciones hipergeométricas; Funciones Heun confluentes; Klein-Gordon equation; Lambert-W potential; Scattering states; Hypergeometric functions; Confluent Heun functions
• Online pristup: http://repositorio.yachaytech.edu.ec/handle/123456789/101