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

## TL;DR

This paper investigates how energy-dependent potentials affect the one-dimensional Klein-Gordon oscillator, analyzing Shannon entropy and Fisher information to reveal features of quantum states.

## Contribution

It introduces a study of Shannon entropy and Fisher information for the Klein-Gordon oscillator with energy-dependent potentials, highlighting new insights into quantum information measures.

## Key findings

- Calculated position and momentum entropies for low-lying states n=0,1,2
- Identified interesting features of Fisher and Shannon densities
- Demonstrated behavior of probability densities

## Abstract

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.