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arXiv:1911.01997

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

Collins Okon Edet, P. O. Amadi, M. C. Onyeaju, U. S. Okorie, R. Sever, Gaotsiwe Joel Rampho, A. N. Ikot

Published Nov 5, 2019• 1 citation
arXivHTMLPDF

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.

DOI
10.48550/arxiv.1911.01997

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In this work, we study an approximate bound state solution of a 2D Schrodinger equation under the influence of external magnetic and Aharonov–Bohm (AB) fields with Hellmann plus screened Kratzer potential (HPSKP) using the Nikiforov–Uvarov-functional- analysis method (NUFA). We obtained the normalised wave function expressed in terms of the Jacobi polynomial. The energy spectra were also obtained in closed form and used to study the energy levels of hydrogen and chromium hydride molecules. The partition function was evaluated using Poisson’s summation approach while other thermomagnetic properties such as free energy, mean energy, entropy, heat capacity, magnetisation, magnetic susceptibility, persistent current at zero and finite temperatures were evaluated analytically.
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In this study, the effects of Aharonov-Bohm (AB) and magnetic fields on the thermodynamic and magneto-transport properties of TiH diatomic molecule using the Deng-Fan potential as a model are investigated. The functional analysis approach (FAA) is used to solve the Schrodinger equation in the presence of magnetic and AB fields with Deng-Fan potential. The energy equation, as well as the wave function, have been derived. The analytic expressions for the thermo-magnetic and transport properties of the Deng-Fan potential are derived using the energy equation and the partition function. These properties obtained are thoroughly analysed utilising graphical representations. Our analysis shows that the magnetic susceptibility of the TiH exhibits a diamagnetic behaviour, and the specific heat capacity behaviour agrees with the famous Dulong-Petit law when the system is subjected to AB field variations and a fixed magnetic field. Albeit, a slight anomaly is observed in the behaviour of the specific heat capacity. Our findings will be valuable in various fields of physics, including chemical and molecular physics and condensed matter physics, where the derived models could be applied to study other diatomic molecules and quantum dots, respectively.