Quantum Information Entropies for the $\ell$-state P\"oschl-Teller-type potential

TL;DR

This paper investigates quantum information measures such as uncertainties, Fisher information, and related inequalities for the P"oschl-Teller-type potential across different angular momentum states, providing numerical and graphical insights.

Contribution

It introduces a comprehensive analysis of uncertainty relations and Fisher information for the P"oschl-Teller-type potential for any angular momentum quantum number.

Findings

Heisenberg uncertainty principle holds for the potential

Fisher-information-based uncertainty relation is valid

Cramer-Rao inequality is satisfied

Abstract

In this study, we obtained the position-momentum uncertainties and some uncertainty relations for the P\"oschl-Teller-type potential for any $\ell$. The radial expectation values of $r^{-2}$, $r^{2}$ and $p^{2}$ are obtained from which the Heisenberg Uncertainty principle holds for the potential model under consideration. The Fisher information is then obtained and it is observed that the Fisher-information-based uncertainty relation and the Cramer-Rao inequality hold for this even power potential. Some numerical and graphical results are displayed.