Analytical solution of the Klein Gordon equation with a Multi-parameter q-Deformed Woods-Saxon Type Potential

Abstract

In this manuscript, we present analytical solution of the Klein-Gordon equation with the multi-parameter q-deformed Woods-Saxon type potential energy under the spin symmetric limit in $(1+1)$ dimension. In the scattering case, we obtain the reflection and transmission probabilities and prove the conservation of the total probability. Moreover, we analyze the correlation between the potential parameters with the reflection and transmission probabilities. In the bound state case, we use the continuity conditions and derive a quantization scheme. To confirm our results numerically, in both cases we randomly assign values to the potential parameters and find numerical results by using the Newton Raphson method.

arXiv comment20 pages, 2 tables and 15 figures

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Cited by in corpus (3)

• A statistical mechanical analysis on the bound state solution of an energy-dependent deformed Hulthén potential energy
• A Comparative Interpretation of the Thermodynamic Functions of a Relativistic Bound State problem proposed with an Attractive or a Repulsive Surface Effect
• On the Role of Differentiation Parameter in a Bound State Solution of the Klein-Gordon Equation