Quantum Information Entropies on Hyperbolic Single Potential Wells

In this work, we study the quantum information entropies for two different types of hyperbolic single potential wells. We first study the behaviors of the moving particle subject to two different hyperbolic potential wells through focusing on their wave functions. The shapes of these hyperbolic potentials are similar, but we notice that their momentum entropy densities change along with the width of each potential and the magnitude of position entropy density decreases when the momentum entropy magnitude increases. On the other hand, we illustrate the behaviors of their position and momentum entropy densities. Finally, we show the variation of position and momentum entropies S-x and S-p with the change of the potential well depth u and verify that their sum still satisfies the BBM inequality relation.

Automated summary

This study examines the quantum information entropies for two different types of hyperbolic single potential wells, revealing that the momentum entropy densities of the wells change with their width and the position entropy density decreases as momentum entropy magnitude increases. Additionally, the variation of position and momentum entropies with potential well depth is investigated, confirming that their sum still satisfies the BBM inequality relation.