Quantum information for a solitonic particle with hyperbolic interaction

TL;DR

This paper investigates a quantum particle with a solitonic mass distribution in a hyperbolic potential, providing analytical solutions and information-theoretic measures for the lowest energy states.

Contribution

It presents analytical solutions for a position-dependent mass quantum system with hyperbolic interaction, including entropy and Fisher information calculations.

Findings

Analytical energy eigenvalues obtained for the system.

Shannon entropy and Fisher information calculated for ground states.

Results demonstrate the quantum information characteristics of solitonic mass particles.

Abstract

In this work, we analyze a particle with position-dependent mass, with solitonic mass distribution in a stationary quantum system, for the particular case of the BenDaniel-Duke ordering, in a hyperbolic barrier potential. The kinetic energy ordering of BenDaniel-Duke guarantees the hermiticity of the Hamiltonian operator. We find the analytical solutions of the Schr\"odinger equation and their respective quantized energies. In addition, we calculate the Shannon entropy and Fisher information for the solutions in the case of the lowest energy states of the system.