# Information entropy as a measure of tunneling and quantum confinement in a symmetric double-well potential

## TL;DR

This paper uses information entropy measures to analyze quantum tunneling and confinement in a symmetric double-well potential, demonstrating that entropy-based uncertainty relations provide better insights than traditional methods.

## Contribution

It introduces an entropy-based approach to quantify quantum phenomena in double-well systems, offering a more effective interpretation than conventional uncertainty products.

## Key findings

- Entropy measures outperform traditional uncertainty in describing tunneling.
- Total entropy and phase-space area increase with barrier height.
- Phase-space analysis offers semiclassical insights into quantum confinement.

## Abstract

Information entropic measures such as Fisher information, Shannon entropy, Onicescu energy and Onicescu Shannon entropy of a symmetric double-well potential are calculated in both position and momentum space. Eigenvalues and eigenvectors of this system are obtained through a variation-induced exact diagonalization procedure. The information entropy-based uncertainty relation is shown to be a better measure than conventional uncertainty product in interpreting purely quantum mechanical phenomena, such as, tunneling and quantum confinement in this case. Additionally, the phase-space description provides a semiclassical explanation for this feature. Total information entropy and phase-space area show similar behavior with increasing barrier height.