Eur. Phys. J. Plus (2018) 133: 528
https://doi.org/10.1140/epjp/i2018-12299-y

Regular Article

Analytical solution of the Klein Gordon equation with a multi-parameter q-deformed Woods-Saxon type potential

¹ Department of Physics, Akdeniz University, 07058, Antalya, Turkey
² Department of Physics, Faculty of Science, University of Hradec Králové, Rokitanského 62, 500 03, Hradec Králové, Czech Republic
³ Theoretical Physics Group, Department of Physics, University of Port Harcourt, P M B 5323, Choba, Port Harcourt, Nigeria
⁴ Department of Mathematics, University of Port Harcourt, Choba, Port Harcourt, Nigeria

^* e-mail: bclutfuoglu@akdeniz.edu.tr

Received: 9 August 2018
Accepted: 5 October 2018
Published online: 19 December 2018

Abstract

In this manuscript, we present an analytical solution of the Klein-Gordon equation with the multi-parameter q-deformed Woods-Saxon type potential energy under the spin symmetric limit in 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.