Thermal properties and Magnetic susceptibility of Hellmann potential in Aharanov-Bohm(AB) flux and Magnetic fields at zero and finite temperatures

TL;DR

This paper investigates the thermal and magnetic properties of a quantum system under Hellmann potential influenced by Aharonov-Bohm flux and magnetic fields, providing analytical solutions and thermodynamic analysis at various temperatures.

Contribution

It presents a closed-form solution for the energy spectrum and wave functions of the system under external fields using functional analysis, and analyzes thermodynamic properties at different temperatures.

Findings

AB flux more effectively removes degeneracy than magnetic field.

Magnetic susceptibility behavior is similar at zero and finite temperatures.

Results are consistent with existing literature in three-dimensional extension.

Abstract

In this research work, the Hellmann potential is studied in the presence of external magnetic and AB-flux fields. We solve the Schrodinger in the presence of these fields and the potential via the functional analysis approach (FAA). The energy equation and wave function of the system are obtained in closed form. The effect of the fields on the energy spectra of the system examined in details. It is found that the AB field performs better than the magnetic in its ability to remove degeneracy. Furthermore, the magnetization and magnetic susceptibility of the system was discussed at zero and finite temperatures. We evaluate the partition function and use it to evaluate other thermodynamic properties of the system such as magnetic susceptibility, Helmholtz free energy,entropy, internal energy and specific heat. A comparative analysis of the magnetic susceptibility of the system at zero and finite temperature shows a similarity in the behavior of the system. A straight forward extension of our results to three dimension shows that the present result is consistent with what is obtains in literature.