Nikiforov Uvarov Research Articles

Electric quadrupole transitions of 98–112Ru atomic nuclei via conformable fractional Bohr Hamiltonian

In this paper, we investigate the energy spectra, wave functions and the [Formula: see text] transition rates for [Formula: see text]Ru atomic nuclei, using the conformable fractional Bohr Hamiltonian model. For the [Formula: see text]-part of the potential, the newly proposed Yukawa plus modified exponential potential is considered and the harmonic oscillator potential in [Formula: see text]-part, with [Formula: see text] fixed around [Formula: see text]. By using the conformable fractional Nikiforov–Uvarov method, energy spectra and wave functions are obtained analytically. The sensitivity of the potential parameters and the spectra with respect to the fractional order parameter is investigated. The normalized fractional energies and fractional electric quadrupole transition rates are compared with the available experimental predictions and those from existing theoretical studies. Comparisons are made at different values of the fractional derivative order. The results are presented across a broader range of values of [Formula: see text], providing a systematic analysis of how variations in this parameter influence the energy spectra, wave functions, and [Formula: see text] transition rates in Ru nuclei. Overall, the comparison of our results with experimental data shows the good accuracy of our model, especially when the fractional parameter goes to lower values. It can be concluded that the order of fractional derivative plays a crucial role in refining theoretical predictions of electric quadrupole transition rates, especially for transitions involving higher multipolarities.

Thermomagnetic Models for the Improved Rosen–Morse Oscillator

ABSTRACTThis study solves the radial Schrödinger wave equation (RSWE) with the improved Rosen–Morse (IRM) potential constrained by an electromagnetic field. Energy eigenvalues are derived using the parametric Nikiforov–Uvarov method and Pekeris approximation. The internal partition function, isobaric molar heat capacity formula, and magnetization model are then deduced from the equation governing pure vibrational energy states. These analytical models are applied to several pure substances, specifically Br2 (X 1Σg+), BrF (X 1Σ+), ICl (X 1Σg+), and P2 (X 1Σg+) molecules. Numerical approximations of the energy eigenvalues for these molecules closely match their exact values. The isobaric molar heat capacity expression yields mean percentage absolute deviations of 1.6585%, 0.9162%, 1.2193%, and 0.7232% when compared against experimental data for Br2 (X 1Σg+), BrF (X 1Σ+), ICl (X 1Σg+), and P2 (X 1Σg+), respectively. These results align well with other heat capacity models in existing literature.

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

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.

Study of heavy quarkonia in the presence of magnetic field by Nikiforov Uvarov method

The N-dimensional radial Schrödinger equation has been solved using the Nikiforov Uvarov (NU) method, in which we used the medium modified form of Cornell potential and quasi-particle Debye mass with strong magnetic field background. The binding energies and the mass spectra of heavy quarkonium have been studied in the N-dimensional space for different values of magnetic field, the binding energy decreases with increasing magnetic field, which shows early dissociation of heavy quarkonium system. The influence of dimensionality number has also been discussed on binding energies of [Formula: see text] and [Formula: see text] for fixed value of magnetic field. It is found that with an increase in dimensionality, the binding energy starts decreasing from a higher initial value. The results obtained are quite consistent with recent studies.

Stark shift in a Frost-Musulin quantum dot: Analytical solution

In the research, a quantum dot (QD) under an external magnetic field is theoretically investigated. The confining potential applied to the charge carriers is chosen as the Frost-Musulin (FM) potential model. First, the energy eigenvalues and eigenstates have been analytically obtained by Nikiforov-Uvarov (NU) procedure. Then, an electric field is imposed on the system. The Stark shift effect (SSE) has been calculated and an analytical relation has been obtained in terms of the Jacobi polynomials. The findings show that the shift of electron energy states at large, and small electric fields are different. The shift is small at weak electric fields. The electron energy states decrease with the increment of the electric field. The electron states are increased by enhancing the system size. In summary, the SSE can be tuned by setting the electric field, the potential height, and the size of QD.

The Application of Spectroscopic Parameters for Computing the Energy Spectrum of Selected Diatomic Molecules (VH, LiH, TiC and CuLi)

A basic theoretical model known as the Schrodinger equation is utilized to explain the physics of the waveform, a phenomenon in quantum mechanics. The whole characterization of a technique’s components is included within the wave function. There are several aspects of the Schrodinger equation’s numerical solution. In this work, we determined mathematically the eigenvalues and characteristic functions of the Eckart-Hellmann potential. This study adopted an estimating strategy for solving the problem recommended by the Nikiforov–Uvarov approach and employed the Greene–Aldrich approximation. The aim was determining bound energies and applying the findings to particular diatomic molecules and their spectroscopic parameters. By contrasting our eigenvalue data with extra numerical data collected by other scholars, the good outcomes of our technique were validated.

Research on nonlinear optical absorption coefficients of GaAs/Ga1−ηAlηAs quantum dots

The effects of quantum dot (QD) radius, incident light intensity, temperature and other factors on the optical absorption coefficients (OACs) of cylindrical QDs are investigated numerically for typical GaAs/Ga[Formula: see text]Al[Formula: see text]As. We theoretically studied the cylindrical QDs with like-inversely quadratic Hellmann potential and parabolic potential. The expressions for the energy levels and wave functions were obtained by the Nikiforov–Uvarov method, and then the expressions for the OACs were derived by using the density matrix theory and the iterative method. Finally, the results show that the structural and external parameters affect the sensitivity of the optical absorption properties by influencing the matrix elements and energy levels, and the quantum confinement effects affect their applicable frequencies, which makes the QD system easier to tune.

Commentary: Solutions of the Schrodinger equation of the shifted screened Kratzer potential and its thermodynamic functions using the extended Nikiforov–Uvarov method

Commentary: Solutions of the Schrodinger equation of the shifted screened Kratzer potential and its thermodynamic functions using the extended Nikiforov–Uvarov method

Effects of magnetic and Aharonov–Bohm flux fields on information entropy with modified Kratzer plus screened Coulomb potential for selected diatomic molecules

The Shannon information entropy for scandium fluoride (ScF) and hydrogen ( H 2 ) molecules in the presence of magnetic and Aharanov–Bohm (AB) fields with modified Kratzer plus screened Coulomb potential in the position and momentum coordinate is investigated. The wavefunction and probability density are obtained by solving the two-dimensional (2D) Schrödinger wave equation using the Nikiforov–Uvarov functional analysis method and then applied to calculate the Shannon entropy. The graphical behaviour of the 2D wavefunction and probability density is showcased. Our results depict the effects of the external fields on Shannon entropy for ScF and ( H 2 ) , the negative values of the position Shannon entropies obtained imply higher localisation of the particles and molecules indicating more stability of the system. Another interesting part of this work is that Bialynicki–Birula–Mycielski inequality is tested and proven bounded for both diatomic molecules. A few to mention, this research will enhance the apprehension of the dynamics of quantum molecules and systems subjected to external fields, quantum information signal processing and communication.

The application of Cornell potential on determining Mass spectra of heavy quarkonium via the Nikiforov–Uvarov method

The mass spectrum of heavy mesons using the Cornell potential is used for studying the quark–antiquark interaction. By appropriately modifying the potential parameters, the established potential models such as Kratzer’s potential and the anharmonic one are applied in the Pekeris approximation. The Schrodinger equation for the Cornell potential setting is solved in this paper via the Nikiforov–Uvarov method. We acquire the confined-state energy spectrum to verify whether the outcome produced by this approach is accurate. The spectrum of energy formulation is used to determine the mass spectra of heavy quarkonium compounds, including charmonium and bottomonium. There is a comparison with various theoretical stances. The outcomes align well with both experimental data and other researchers’ findings.

Investigating the fractional wave function and the impact of topological defects with anisotropic plasma on the dissociation of bottomonium in the fractional non-relativistic quark model

Incorporating a topological defect and anisotropic plasma, this work used the generalized fractional of the Nikiforov–Uvarov technique to solve the fractional-radial Schrödinger equation in the longitudinal-transverse plane. The study produced wave functions and energy eigenvalues in their fractional forms. The results showed that the presence of an anisotropic plasma and a topological defect increases the dissociation energy of bottomonium. Furthermore, regardless of whether the fractional or classical models are taken into account, it was shown that the effect of temperature on the dissociation energy is stronger than the effect of baryonic chemical potential. In addition, the dissociation energy of bottomonium is significantly larger at lower chemical potential levels. Last but not least, the energy of bottomonium is only little influenced by magnetic auxiliaries.

Analytical Solutions of the D-dimensional Klein-Gordon equation with q-deformed modified P¨oschl-Teller Potential

In this article, the D-dimensional Klein-Gordon equation within the framework of Greene-Aldrich approximations scheme for q-deformed modified P¨oschl-Teller Potential is solved for s-wave and arbitrary angular momenta. The energy eigenvalues and corresponding wave functions are obtained in an exact analytical manner via the Nikiforov-Uvarov (N-U) method. Further, it is shown that in the non-relativistic limit, the energy eigenvalues reduce to that of Schrodinger equations for the potential. It is also shown that, the obtained results lead to the solutions of the same problem for modified P¨oschl-Teller potential for \(q = 1\).

Analytical solutions for the Klein–Gordon equation with combined exponential type and ring-shaped potentials

In this study, we have successfully obtained the analytical solutions for the Klein–Gordon equation with new proposed a non-central exponential potential Vr=D1-σ0coth(αr)2+(η1+η2cosθ)/r2sin2θ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$V\\left( r \\right) = D\\left[ {1 - \\sigma_{0} \\coth (\\alpha r)} \\right]^{2} + (\\eta_{1} + \\eta_{2} \\cos \ heta )/r^{2} \\sin^{2} \ heta$$\\end{document}. Our approach involves a proper approximation of the centrifugal term, with l′\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${l}{\\prime}$$\\end{document} representing the generalized orbital angular momentum quantum number, and the utilization of the Nikiforov–Uvarov method. The resulting radial and angular wave functions are expressed in terms of Jacobi polynomials, and the corresponding energy equation is also derived. Our calculations of the eigenvalues for arbitrary quantum numbers demonstrated significant sensitivity to potential parameters and quantum numbers. Additionally, we evaluate the dependence of energy eigenvalues on screening parameter α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha$$\\end{document} for arbitrary quantum numbers nr\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n_{r}$$\\end{document} and N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$N$$\\end{document} to establish the accuracy of our findings. Furthermore, we determine the non-relativistic limits of the radial wave function and energy equation, which align with corresponding previous results in the case where η1=η2=0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\eta_{1} = \\eta_{2} = 0$$\\end{document}.

On the fractional quark–antiquark confinement and symplectic quantum mechanics

Using the formalism of generalized fractional derivatives, a two-dimensional nonrelativistic meson system is studied. The mesons are interacting by a Cornell potential. The system is formulated in the domain of the symplectic quantum mechanics by means of the generalized fractional Nikiforov–Uvarov method. The corresponding Wigner function and the energy eigenvalues are then derived. The effect of fractional parameters [Formula: see text] and [Formula: see text] with the ground state solution is analyzed through the Wigner function for the charm–anticharm, bottom–antibottom and [Formula: see text] mesons. One of the fundamental achievements of such Cornell model is the determination of heavy quarkonia mass spectra. We have computed these masses and the present results are in agreement with the experimental data, improving previous theoretical results.

Exact solutions of position-dependent mass Schrödinger equation with pseudoharmonic oscillator and its thermal properties using extended Nikiforov–Uvarov method

Exact solutions of position-dependent mass Schrödinger equation with pseudoharmonic oscillator and its thermal properties using extended Nikiforov–Uvarov method

Impact of topological defects and Yukawa potential combined with inverse square on eigenvalue spectra of diatomic molecules O 2, NO, LiH, HCl

In this paper, we investigate a quantum system composed of non-relativistic particles interacting with an external potential while in the presence of a topological defect produced by a point-like global monopole. We derive the radial equation of the Schrödinger equation for this system, considering a Yukawa potential combined with inverse square potential within the backdrop of a point-like global monopole. To determine the eigenvalue solutions for this quantum system, we employ a suitable approximation scheme known as the Pekeris approximation. This approximation is applied to the centrifugal term, and we solve the resulting radial equation using the parametric Nikiforov-Uvarov (NU) method. Subsequently, we examine the quantum system when only Yukawa potential is present, and we obtain the eigenvalue solutions using the same procedure. In both cases, we observe that the presence of the global monopole topological defect has a significant impact on the energy spectrum of quantum particles interacting with an external potential. To illustrate this effect, we consider a few diatomic molecules, such as O 2, NO, LiH, and HCl. We present the energy spectrum and compare our results with previously published findings in the literature. Furthermore, we generate several plots to visually depict the influence of the global monopole on the energy eigenvalues for these different molecules.

The complete solution of the Schrödinger equation with the Rosen–Morse type potential via the Nikiforov–Uvarov method

We determine exact solutions of the time-independent Schrödinger equation for the Rosen–Morse type potential by using the Nikiforov–Uvarov method. This method allows us to write the eigenfunctions of the Schrödinger equation as the product of two simpler functions in a constructive way. The resolution of this problem is used to show that the kinks of the non-linear Klein–Gordon equation with φ2p+2 type potentials are stable. We also derive the orthogonality and completeness relations satisfied by the set of eigenfunctions, which are useful in the description of the dynamics of kinks under perturbations or interacting with antikinks.

Solutions of Schrödinger equation based on Modified Exponential Screened Plus Yukawa Potential (MESPYP) within the frame of parametric Nikiforov-Uvarov method

In this paper, we deduced an approximate bound state solutions of Schrӧdinger equation based on Modified Exponential Screened Plus Yukawa Potential (MESPYP), with the help Greene–Aldrich Approximation to determine the centrifugal term. The analytical solution was obtained based on Nikiforov–Uvarov (NU) method. The bound state solutions of five diatomic molecules which are mercury hydride (HgH), zinc hydride (ZnH), cadmium hydride (CdH), hydrogen bromide (HBr) and hydrogen fluoride (HF) molecules were also calculated numerically. The estimated energy eigenvalues for these molecules were deduced using the resulting energy eigenequation and total unnormalized wavefunction is expressed in term of Jacobi polynomial. The numerical solution shows that the bound state solutions increase with increase in the quantum state.

Dirac particles with screened Kratzer–Hulthen plus ring-shaped potential in noncompact extra dimensions

To describe the four fundamental interactions observed in the universe, we used the Dirac equation containing an interaction of the screened Kratzer and the Hulthen potential with a ring-shaped term. We study the energy spectra of spin-[Formula: see text] particles in noncompact extra dimensions. The polar and angular parts of the N-dimensional Dirac equation are solved using the Nikiforov–Uvarov method. The transcendental energy equation and the associated two components spinor wavefunctions of the spin-[Formula: see text] particles are obtained. Moreover, we obtained the nonrelativistic limit of our results by mean of a specific mapping. Some special cases of the proposed potential have been discussed, and their corresponding eigenvalue energies were determined. Finally, we proposed that our results can be used in many branches of physics, to investigate scenarios in extra dimensions where spin-[Formula: see text] particles are involved. To test the reliability of our model, we computed the numerical values of the energy spectra of lithium hydride and hydrogen chloride diatomic molecules using a special case of the proposed potential. The energy spectra are calculated for different quantum numbers [Formula: see text] at different values of the dimensionality of the space. The results of this research are overall in good agreement with the theoretical studies of similar investigation.

Ro-vibrational energy spectra and thermal properties of some diatomic molecules

The present work deals with the solutions to the radial Schrodinger equation for harmonic plus screened Kratzer potential (HSKP) within the framework of the Nikiforov–Uvarov functional analysis method. The Greene–Aldrich approximation is used to handle the inverse square terms of the HSKP. Reducing the HSKP into Kratzer and screened Kratzer potentials, the energy spectra of selected diatomic molecules, i.e. LiH, HCl, O 2 and I 2 are computed. Further, the equations for expectation values of several parameters, including inverse of position ( r − 1 ), square of inverse of position ( r − 2 ), kinetic energy (T) and the square of momentum ( p 2 ) are obtained invoking the Hellmann–Feynman theorem. Results of this study are consistent with other similar previous studies. The analytical expressions for partition function and other thermodynamic properties of the diatomic molecules are determined.