The Nikiforov-Uvarov method in the study of thermodynamic properties of the diatomic molecules
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Authors
Ramantswana, Morris
Issue Date
2024-02
Type
Thesis
Language
en
Keywords
Aharonov-Bohm flux , Diatomic molecules , Hulth´en potential , Magnetic fields , Manning-Rosen potential , Nikiforov-Uvarov method , Partition function , Schr¨odinger equation , Thermodynamic properties , Yukawa potential , Natural Sciences (Biotechnological studies) , SDG 7 Affordable and Clean Energy
Alternative Title
Abstract
Transition metal hydrides, including CrH and others, have a significant impact on
chemical synthesis, serving as intermediates and in solid matrix samples for infrared
spectroscopy. Moreover, the CuLi molecule provides insights into the bonding characteristics
of mixed transition metal lithides. Additionally, the study of transition metal
carbide molecules like TiC, NiC, and others is currently a highly active research area,
driven by the necessity for accurate measurement of their chemical bonding.
This thesis explores the solution of the Schr¨odinger equation for the Manning-Rosen
potential alongside a class of Yukawa and the Hulth´en plus Yukawa potential models
using the Nikiforov-Uvarov method. It obtains the energy eigenvalues and corresponding
eigenfunctions in closed form. Subsequently, the partition function is computed,
and various thermodynamic functions such as Helmholtz free energy, mean energy, entropy,
and specific heat capacity of the system are evaluated.
Furthermore, the Schr¨odinger equation for the Hulth´en plus Yukawa potential model
is solved under the influence of magnetic and Aharonov-Bohm flux fields using the exact
quantization rule. Closed-form expressions for the energy eigenvalues are derived
and utilized to compute the partition function and other thermo-magnetic functions
such as Helmholtz free energy, mean energy, entropy, specific heat, magnetization, and
magnetic susceptibility for CuLi, CrH, and NiC diatomic molecules. These findings
are relevant in condensed matter physics, chemical and molecular physics, and various
other areas of physics.