# Quantum confinement in an asymmetric double-well potential through energy analysis and information entropic measure

## TL;DR

This paper investigates particle localization in asymmetric double-well potentials using energy analysis and information entropy measures, revealing how asymmetry influences localization and the transition to symmetric configurations.

## Contribution

It introduces a general rule for quasi-degenerate pairs based on asymmetry and demonstrates how information entropy and phase-space analysis elucidate localization behavior.

## Key findings

- States localize to the deeper well beyond a threshold asymmetry.
- Eigenfunctions and eigenvalues are accurately obtained via a variation-induced diagonalization.
- Asymmetry causes wells to behave as distinct potentials, affecting particle distribution.

## Abstract

Localization of a particle in the wells of an asymmetric double-well (DW) potential is investigated here. Information entropy-based uncertainty measures, such as Shannon entropy, Fisher information, Onicescu energy, etc., and phasespace area, are utilized to explain the contrasting effect of localization-delocalization and role of asymmetric term in such two-well potentials. In asymmetric situation, two wells behaves like two different potentials. A general rule has been proposed for arrangement of quasi-degenerate pairs, in terms of asymmetry parameter. Further, it enables to describe the distribution of particle in either of the deeper or shallow wells in various energy states. One finds that, all states eventually get localized to the deeper well, provided the asymmetry parameter attains certain threshold value. This generalization produces symmetric DW as a natural consequence of asymmetric DW. Eigenfunctions, eigenvalues are obtained by means of a simple, accurate variationinduced exact diagonalization method. In brief, information measures and phase-space analysis can provide valuable insight toward the understanding of such potentials.