Determination of Fisher and Shannon Information for 1D Fractional Quantum Harmonic Oscillator

TL;DR

This paper calculates Fisher information and Shannon entropy for a 1D fractional quantum harmonic oscillator using Riesz-Feller derivatives, offering new insights into its probabilistic characteristics.

Contribution

It introduces a method to compute Fisher and Shannon parameters for fractional quantum systems using Riesz-Feller derivatives, which is novel in this context.

Findings

Derived Fisher information for the fractional oscillator

Calculated Shannon entropy for the fractional oscillator

Provided insights into the probabilistic behavior of fractional quantum systems

Abstract

This study employs the Riesz-Feller fractional derivative to determine Fisher and Shannon parameters for a one-dimensional harmonic oscillator. By deriving the Riesz fractional derivative of the probability density function, we quantify both Fisher information and Shannon entropy, thus providing valuable insights into the system's probabilistic nature.