Analytical Solutions of the Klein-Gordon equation and Fisher information with Inversely Quadratic Hellman potential

The inversely quadratic Hellman (IQH) potential has gained recognition in recent times. This paper is focused on the analytical solutions of the Klein-Gordon equation with the IQH potential and its application to Fisher information. Using the parametric form of the Nikiforov-Uvarov method, the relativistic and non-relativistic energies of the IQH potential are obtained, along with the wave functions. Furthermore, the Fisher information measure and uncertainty of the system are obtained. Our results show that the momentum space probability density function is more localized. This is confirmed to be true by the high values of the Fisher information in momentum space. Furthermore, the occurrence of squeezed states is observed. The uncertainty results and the Fisher information show that the system is stable.