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

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