Theoretical computation of eigenenergies, expectation values and thermodynamic functions of shifted Deng-Fan-Hellmann potential in external fields

Abstract

Using the Nikiforov-Uvarov functional analysis (NUFA) method, we determined the energy eigenvalues and corresponding normalized eigenfunctions for a newly proposed shifted Deng-Fan-Hellmann potential in the presence of external magnetic and Aharonov-Bohm (AB) flux fields for H₂, HCl, and CO molecules. Furthermore, we investigated the combined effect of magnetic and AB flux fields on the energy spectrum’s degeneracy. We have also obtained the energy eigenvalues for the special cases and cross-referenced them with findings from other studies to validate the accuracy of our analytical calculations. Using the Hellman-Feynman theorem, we derived expressions for the expectation values of the square of the inverse of position $\left(r^{-2}\right)$, kinetic energy $\left(T\right)$, and square of momentum $\left(P^2\right)$, along with their respective numerical values for the selected molecules. Additionally, we have obtained the thermomagnetic properties for the molecules using the energy eigenvalues. Our results are in line with the findings documented in the existing literature.