Shannon Entropy and Fisher Information of the one-dimensional Klein-Gordon oscillator with energy-dependent potential

In this paper, we studied, at first, the influence of the energy-dependent potentials on the one-dimensionless Klein-Gordon oscillator. Then, the Shannon entropy and Fisher information of this system are investigated. The position and momentum information entropies for the low-lying states n=0,1,2 are calculated. Some interesting features of both Fisher and Shannon densities as well as the probability densities are demonstrated.