arXiv subjects

A. N. Ikot

Publications and source records attributed to A. N. Ikot.

18 recordsLinked to original sources

arXiv2025

Spectral and Thermal Analysis of the Morse Potential within the Dunkl Formalism: Analytical Approximations and Applications

In this work, we investigate the quantum dynamics of a particle subject to the Morse potential within the framework of Dunkl quantum mechanics. By employing the Dunkl derivative operator, which introduces reflection symmetry, we construct a deformed Schrödinger equation and obtain exact analytical solutions using the Pekeris approximation. The resulting energy spectrum and wavefunctions reveal how Dunkl parameters alter the effective potential and vibrational states. The model is applied to several diatomic molecules, including H$_2$, HCl, and I$_2$, illustrating the impact of symmetry deformation on energy spectra. We also compute thermodynamic functions, including the partition function, free energy, internal energy, entropy, and specific heat. The analysis shows that the Dunkl deformation induces distinct thermal behavior and offers a tunable approach to molecular modeling. These results highlight the potential of the Dunkl formalism as a useful tool for extending conventional quantum models and for exploring symmetry-deformed systems in molecular physics and quantum thermodynamics.

quant-ph↗

arXiv2024

The Performance Analysis of a Quantum-Mechanical Carnot-like Engine using Diatomic Molecules

This study presents an analysis of a quantum mechanical formulation of the Carnot like cycle using diatomic molecules, i.e., the Morse oscillator, as the working substance. The generalized model with an arbitrary one dimensional potential is used to obtain the important performance parameters such as the efficiency, the power output, and the optimal region of the engine by considering well width L moving with a finite speed. The optimal efficiency, the maximum power output, and dimensionless power ranges of the working substance was also determined. The results obtained in this work are found to agree with those obtained for similar engine but with different working substance.

quant-ph↗

arXiv2023

Quantum flux effects on the energy spectra and thermo-magnetic properties in 2D Schrodinger equation with Mobius square potential

A 2D Schrodinger equation with interacting Mobius square potential model is solved using Nikiforov-Uvarov Functional Analysis (NUFA) formalism. The energy spectra and the corresponding wave function for the linearly and exponentially varying quantum magnetic flux are obtained analytically in a closed form. The evaluated energy spectra are used to obtain an expression for the partition functions for the two cases comprises of the linearly and exponentially varying quantum magnetic flux and vis-a-vis is use to evaluate other thermodynamic and magnetic properties for the system. The results are used to study the free energy, mean energy, the entropy, specific heat, magnetization, magnetic susceptibility and the persistent current of the system. The numerical bound state energies are computed.

quant-ph↗

arXiv2022

The efficiency of Quantum Mechanical Carnot Engine using the Woods Saxon model

The quantum engine cycle serves as an analogous representation of classical heat engines for microscopic systems and the quantum regime of thermal devices is composed of a single element. In this work, the Quantum-Mechanical properties of a non-linear quantum oscillator described by the Woods-Saxon [WS] model are examined. The Quantum-Mechanical analogue of the Carnot cycle was constructed using changes in both the width L of the well and the quantum state of the potential well. The efficiency of the quantum engine, consisting of adiabatic and isothermal processes based on the Woods-Saxon [WS] potential is derived. The result is shown to be analogous to that of the classical engine and found to agree, within an appropriate limit, with existing results obtained from other potential models. This implies that the [WS] potential can be used as an alternative model in quantum engines.

quant-ph↗

arXiv2022

Confinement Effects of External Fields and Topological Defect on Hydrogen Atom in a Quantum-plasma Environment

This study looks at the confinement effects of Aharonov-Bohm (AB) flux and magnetic fields, as well as topological defects in a quantum plasma, on the hydrogen atom. The joint effects show that the system is extremely attractive. Furthermore, as we've shown, the joint effect of the fields is greater than the sum of the individual effects, resulting in a significant change in the system's bound state energy. The magnetic field can be used as a control parameter or booster, whereas the topological defect and AB field are needed to hold the hydrogen atom in quantum plasmas at a low energy. The findings of our research may be extended to atomic structure and plasma collisions.

physics.plasm-ph↗

arXiv2021

Effects of Topological Defect on the Energy Spectra and Thermo-magnetic Properties of CO Diatomic Molecule

Confinement effects of Aharonov-Bohm (AB) flux and magnetic fields with topological defect on CO diatomic molecule modeled by screened modified Kratzer potential is investigated in this paper. The all-encompassing effects of the fields and topological defect result in a strongly repulsive system. We discover that the collective effect of the fields and defect is intense than the lone and dual effect and consequently there is a substantial shift in the bound state energy of the system. We also find that to sustain a low-energy medium for the molecule modeled by SMKP, the topological defect and weak AB field are required, whereas the Magnetic field can be used as a control parameter or enhancer. The effects of the topological defect and magnetic and AB fields on the thermal and magnetic properties of the system are duly analyzed. We observe that the system tends to exhibit both a paramagnetic and diamagnetic behavior for weak and intense magnetic field respectively and some sort of saturation at large magnetic field. To further validate our findings, we map our result to 3D and a comparison of our results with what obtains in literature reveals an excellent agreement.

quant-ph↗

arXiv2020

Thermal Properties of Deng-Fan-Eckart Potential model using Poisson Summation Approach

The Deng-Fan-Eckart (DFE) potential is as good as the Morse potential in studying atomic interaction in diatomic molecules. By using the improved Pekeris-type approximation, to deal with the centrifugal term, we obtain the bound-state solutions of the radial Schrödinger equation with this adopted molecular model via the Factorization Method. With the energy equation obtained, the thermodynamic properties of some selected diatomic molecules(H2 , CO , and ScN ) were obtained using Poisson summation method.. The unnormalized wave function is also derived. The energy spectrum for a set of diatomic molecules for different values of the vibrational n and rotational l are obtained. To show the accuracy of our results, we discuss some special cases by adjusting some potential parameters and also compute the numerical eigenvalue of the Deng-Fan potential for comparison sake. However, it was found out that our results agree excellently with the results obtained via other methods.

physics.chem-ph↗

arXiv2020

Energy spectra and thermal properties of diatomic molecules in the presence of magnetic and AB fields with improved Kratzer potential

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 three selected diatomic molecules (H2, HCl and LiH). 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.

quant-ph↗

arXiv2020

Approximate Solutions of the Fractional Schrodinger Equation for the Screened Kratzer Potential

By employing the concept of conformable fractional Nikiforv-Uvarov (NU) method, we solved the fractional Schrodinger equation with the screened Kratzer potential (SKP). By applying the Greene-Aldrich approximation and a coordinate transformation schemes, the analytical expressions of the bound state energy spectra and eigenfunctions for SKP were obtained. Numerical results for the energies of SKP for lithium hydride and hydrogen chloride diatomic molecules were computed for different fractional parameters. Also, the graphical variation of the bound state energy eigenvalues of SKP for LiH with different potential parameters and quantum numbers were discussed, as regards the selected fractional parameters. Our results are new and have not been reported in any literature before.

physics.chem-ph↗

arXiv2020

Superstatistics of the screened Kratzer potential with Modified Dirac Delta and Uniform Distributions

We solve the Schrodinger equation to obtain the energy eigenvalues expression of the screened Kratzer potential (SKP) model. With the energy eigenvalues, we evaluated for the partition function within the framework of superstatistics and extended to study the thermodynamic function for some selected diatomic molecules including HCl, LiH and H2. The modified Dirac delta and uniform distribution comparatively in each case in the absence and the presence of the deformation parameter were considered.

physics.chem-ph↗

arXiv2019

Thermodynamic properties of the Superstatistics and Normal Statistics of the Schrodinger Equation with generalized trigonometric Poschl Teller potential

Analytical solutions of the Schrodinger equation for the generalized trigonometric Poschl Teller potential by using an appropriate approximation to the centrifugal term within the framework of the Functional Analysis Approach have been considered. Using the energy equation obtained, the vibrational partition function was calculated and other relevant thermodynamic properties. More so, we use the concept of the superstatistics to also evaluate the thermodynamics properties of the system. It is noted that the well-known normal statistics results are recovered in the absence of the deformation parameter and this is displayed graphically for the clarity of our results. We also obtain analytic forms for the energy eigenvalues and the bound state eigenfunction solutions are obtained in terms of the hypergeometric functions. The numerical energy spectra for different values of the principal and orbital quantum numbers are obtained. To show the accuracy of our results, we discuss some special cases by adjusting some potential parameters and also compute the numerical eigenvalue of the trigonometric Poschl Teller potential for comparison sake. However, it was found out that our results agree excellently with the results obtained via other methods

quant-ph↗

arXiv2019

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

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.

cond-mat.stat-mech↗

arXiv2019

Dissociation of Nucleon and Heavy-Baryon in an Anisotropic Hot and Dense QCD Media Using Nikiforov-Uvarov Method

By using the Nikiforov-Uvarov method, the hyper-radial Schrodinger equation is analytically solved, in which the real modified potential is employed at finite temperature and baryon chemical potential. The eigenvalue of energy and corresponding wave function are obtained in the isotropic and anisotropic media in hot and dense media. The present results show that the binding energy of nucleon and some heavy baryon decrease strongly in hot medium and decreases slightly with increasing baryon chemical potential. In addition, binding energy for each baryon is more bound in an anisotropic medium in comparison with its value in an isotropic medium. The dissociation of temperature of each baryon is above a critical temperature and it increases in the anisotropic medium. The dissociation of temperature is slightly decreased in the hot medium when the baryon of chemical potential is considered. A comparison is studied with the available studies. We conclude that the present study provides a good description of the nucleon and some heavy baryon in hot and dense media in the isotropic and anisotropic systems.

hep-ph↗

arXiv2019

Superstatistics of Schrödinger Equation with Pseudoharmonic potential in an External Magnetic and Aharanov-Bohm(AB) Fields

In this work, the thermodynamic property of pseudoharmonic potential in the presence of external magnetic and AB fields is investigated. We used effective Boltzmann factor within the superstatistics formalism to obtain the thermodynamic properties such as Helmholtz free energy (F), Internal energy (U), entropy(S) and specific heat (C) of the system. In addition, we discuss the result of the thermodynamic properties of some selected diatomic molecules of N2, Cl2, I2 and CH using their experimental spectroscopic parameters and that of the variation of the deformation parameter of q=0,0.3,0.7. We also illustrated with some graphs for clarity of our results in both cases.

quant-ph↗

arXiv2019

Analytic Solution of Multi-Dimensional Schrodinger in Hot and Dense QCD Media Using SUSYQM Method

The N-radial Schrödinger equation is analytically solved by using SUSYQM method, in which the heavy quarkonia potential is introduced at finite temperature and baryon chemical potential. The energy eigenvalue is calculated in the N-dimensional space. The obtained results show that the binding energy strongly decreases with increasing temperature and is slightly sensitive for changing baryon chemical potential up to 0.6 GeV at higher values of temperatures. We employed the nonperturbative corrections to the leading-order of the Debye mass at finite baryon chemical potential. We found that the binding energy is more dissociates when the nonperturbative corrections are included with the leading-order term of Debye mass in both hot and dense media. A comparison is discussed with other works such as the lattice parameterized of Debye mas. Thus, the present potential with the SUSYQM method provides satisfying results for the description of the dissociation of binding energy for heavy quarkonia in hot and dense media.

hep-ph↗

arXiv2018

Analytical solution of the Klein Gordon equation with a Multi-parameter q-Deformed Woods-Saxon Type Potential

In this manuscript, we present analytical solution of the Klein-Gordon equation with the multi-parameter q-deformed Woods-Saxon type potential energy under the spin symmetric limit in $(1+1)$ dimension. In the scattering case, we obtain the reflection and transmission probabilities and prove the conservation of the total probability. Moreover, we analyze the correlation between the potential parameters with the reflection and transmission probabilities. In the bound state case, we use the continuity conditions and derive a quantization scheme. To confirm our results numerically, in both cases we randomly assign values to the potential parameters and find numerical results by using the Newton Raphson method.

quant-ph↗

arXiv2017

Approximate Analytical Solutions of the Effective Mass Klein-Gordon Equation for Yukawa potential

The analytical solutions of the Klein-Gordon equation with the Yukawa potential is presented within the framework of an approximation to the centrifugal potential for any arbitrary state with the position-dependent mass using the parametric Nikiforov-Uvarov method. The energy eigenvalues and the corresponding wave function have been obtained. The energy for both the scalar potential and vector potential as well as the effect of the screening parameter on each of the energy for scalar potential and vector potential are investigated in detail. The nonrelativistic limit is obtained and numerical results are computed. It is found that our results for the constant mass and that of the nonrelativistic limit are in good agreement with the one in the literature.

quant-ph↗

arXiv2017

Klein-Gordon equation particles in exponential-type molecule potentials and its thermodynamic properties in D- dimensions

In this paper we use the Nikiforv-Uvarov method to obtain the approximate solutions of the Klein-Gordon equation with deformed five parameter exponential type potential (DFPEP) model. We also obtain the solutions of the Schrödinger equation in the presence of the DFPEP in the non-relativistic limits. In addition, we calculate in the nonrelativistic limits the thermodynamics properties such as vibrational mean energy U, free energy F and the specific heat capacity C . Special cases of the potential are also discussed.

quant-ph↗