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Mathematics

A Non-Relativistic 2D Quantum System and Its Thermo-Magnetic Properties with a Generalized Pseudo-Harmonic Oscillator

Haifa I. Alrebdi, Akpan N. Ikot, R. Horchani, U. S. Okorie

Published Aug 24, 2024• 5 citations
Publisher

Abstract

In this work, we examine the thermo-magnetic characteristics and energy spectra of a system exposed to both magnetic and Aharonov–Bohm (AB) fields with the existence of an interaction potential that is pseudo-harmonic. Explicit calculations of the eigen-solutions are performed with the expanded Nikiforov–Uvarov formalism. The confluent Heun function is used to represent the equivalent wave functions. If the AB and magnetic fields are gone, quasi-degeneracy in the system’s energy levels is shown by a numerical analysis of the energy spectrum. Additionally, we provided a visual representation of how the AB and magnetic fields affected the system’s thermo-magnetic characteristics. Our results show a strong dependence of thermo-magnetic properties on temperature, screening parameters, external magnetic fields, and AB fields.

DOI
10.3390/math12172623

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We study the effects of the perpendicular magnetic and Aharonov—Bohm (AB) flux fields on the energy levels of a two-dimensional (2D) Klein—Gordon (KG) particle subjected to an equal scalar and vector pseudo-harmonic oscillator (PHO). We calculate the exact energy eigenvalues and normalized wave functions in terms of chemical potential parameter, magnetic field strength, AB flux field, and magnetic quantum number by means of the Nikiforov—Uvarov (NU) method. The non-relativistic limit, PHO, and harmonic oscillator solutions in the existence and absence of external fields are also obtained.
We investigate the thermo-magnetic properties of the Attractive Radial Potential (ARP) for a particle moving in two-dimensional non-relativistic Schrödinger equation subjected to an external magnetic field and Aharonov-Bohm (AB) flux. Analytical solution for the energy eigenvalues and wavefunctions were obtained in a closed form via the Nikiforov-Uvarov Functional Analysis (NUFA) method. We derived the partition function by analyzing the system as a canonical ensemble to obtain the expressions for the thermodynamic quantities which include the free energy, entropy, specific heat capacity and internal energy. Our results show a decrease in the energy spectrum when the AB flux and magnetic fields are increased. At low temperatures, specific heat capacity shows a peak anomaly, while Helmholtz free energy and entropy exhibit temperature dependence. We also observed that AB flux and magnetic field influence both magnetization and magnetic susceptibility and exhibit both paramagnetic and diamagnetic behavior. The findings provide valuable insights into in molecular physics applications.
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.
Abstract Attempts to understand the behaviour of various quantum systems are still become interest for many researchers in recent years. While experimentation is too complicated to be done, analytical mathematical approach is become a reliable choice. This approach is using potential functions or models as representations of the real quantum system, such as physical force interactions within a molecule. In this study, the new combination model of screened Kratzer and screened Eckart potentials is investigated under the non-relativistic quantum mechanics framework. These potentials are well-suited for modelling atomic interactions in diatomic molecules. The primary objective is to examine how these interactions are affected by the presence of external magnetic fields. Using a specific form of the Schro dinger equation, both the energy eigenfunction and the wave function have been derived. The Nikiforov-Uvarov Functional Analysis (NUFA) method was employed for this derivation. Additionally, several thermodynamic properties were obtained from the energy equation using numerical methods. Selected diatomic molecule data were used in the computations to demonstrate the effect of the magnetic field. A detailed analysis was performed through graphical representations, revealing that an increase in the magnetic field or the associated Aharonov-Bohm (AB) flux enhances and splits the energy spectra. The effects on thermodynamic properties vary across different molecules and conditions, but overall, the magnetic field increases the thermodynamic properties of the molecules.
In this study, we employ the extended Nikiforov–Uvarov method to solve the d-dimensional Schrödinger equation with exponential pseudo-harmonic potential. With the help of Greene–Aldrich approximation scheme, analytical expression of the approximate energy eigenvalues and wave function was obtained in closed form and in terms of confluent Heun function, respectively. In addition, expressions of partition function and other thermodynamic functions for the exponential pseudo-harmonic potential were obtained, as they relate with temperature, screening parameter and dimensionality. Numerical and graphical variations of the energies and thermodynamic functions have been presented for various quantum states, temperature, screening parameter and dimensionality values. It is observed that energy eigenvalues and thermodynamic functions of the exponential pseudo-harmonic potential are significantly affected by the screening parameters, dimensionality, temperature and quantum state values considered. Special results for pseudo-harmonic and harmonic potentials are realized as the screening parameter approaches zero. Our results agree with some physical phenomena in condensed matter and atomic physics.
In the present study, the improved screened Kratzer potential (ISKP) is investigated in the presence of external magnetic and Aharanov-Bohm (AB) fields within the framework of non-relativistic quantum mechanics. The Schrodinger equation is solved via the Nikiforov-Uvarov Functional Analysis (NUFA) method and the energy spectra and the corresponding wave function for the ISKP in the presence of external magnetic fields are obtained in a closed form. The obtained energy spectra are used to study some selected diatomic molecules. It is observed that the present of the magnetic and AB fields removes the degeneracy for different values of the control parameter. The thermodynamic and magnetic properties of the ISKP in the present of the magnetic and AB fields are also evaluated. The effects of the control potential parameter on the thermodynamic and magnetic properties of the selected diatomic molecules are discussed.