Parametric Nikiforov-Uvarov Method Research Articles

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.

Shannon entropy and thermodynamic properties of an inversely quadratic Yukawa potential model

An inversely quadratic Yukawa potential is an exponential-type potential that has received little attention only in the bound state to the best of our understanding. This study obtained the solution of the Schrödinger equation for an inversely quadratic Yukawa potential via parametric Nikiforov-Uvarov method and supersymmetric approach. Some thermodynamic properties (vibrational enthalpy, vibrational Gibbs free energy and vibrational entropy) for the Inversely quadratic Yukawa potential are examined. The study is also applied to shannon entropy as the theoretic quantity. The results obtained showed that the energy eigenvalue for the potential goes in the opposite direction with the quantum state and the screening parameter. The Shannon entropy obtained as a function of the potential strength only obeyed the Heinsenberg principle at the ground state and excited states. In both cases, the also satisfied Bialynick-Birula, Mycielski inequality. It is noted that the thermal properties studied as a function of the temperature, even though the studied potential is not a molecular potential, the results followed the trend of the molecular potential.

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.

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.

Diatomic molecular energy spectra and thermodynamic properties of exponential inversely quadratic plus improved deformed exponential-type potential

By employing the Pekeris-type approximation to deal with the centrifugal term, we study the thermodynamic properties and approximate analytical solutions of the Schrödinger equation with the exponential inversely quadratic plus improved deformed exponential-type potential using parametric Nikiforov–Uvarov method and hypergeometric functional analysis method. The complex eigen energy equation was presented in a closed and compact form and extended to study partition function and other thermodynamic properties. The total normalized wave functions were also obtained and expressed in terms of hypergeometric Jacobi polynomial. The mathematical accuracy of analytical calculation can be verified consistently by comparing numerical data and results of different arbitrarily l state. The potential also reduces to improved deformed exponential-type potential as a special case. We calculated energy spectra for some selected diatomic molecules namely: Silicon Flouride (SiF+ (X1∑+), Oxygen molecule O2+ (X2∏g), Nitrogen molecule, N2+ (X1∑g+), Sulphur chloride SCl and Rubidium hydride RbH using standard molecular spectroscopic constants as applied to the two methods. The results show that the energy eigenvalues for these selected diatomic molecules are in excellent agreement using the two methods and also increases with an increase in quantum state.

Arbitrary $$\ell$$-state solutions of the Klein–Gordon equation with the Eckart plus a class of Yukawa potential and its non-relativistic thermal properties

We report bound-state solutions of the Klein–Gordon equation with a novel combined potential, the Eckart plus a class of Yukawa potential, by means of the parametric Nikiforov–Uvarov method. To deal the centrifugal and the coulombic behavior terms, we apply the Greene–Aldrich approximation scheme. We present any $$\ell$$ -state energy eigenvalues and the corresponding normalized wave functions of a mentioned system in a closed form. We discuss various special cases related to our considered potential which are utility for other physical systems and show that these are consistent with previous reports in literature. Moreover, we calculate the non-relativistic thermodynamic quantities (partition function, mean energy, free energy, specific heat and entropy) for the potential model in question, and investigate them for a few diatomic molecules. We find that the energy eigenvalues are sensitive with regard to the quantum numbers $$n_r$$ and $$\ell$$ as well as the parameter $$\delta$$ . Our results show that energy eigenvalues are more bounded at either smaller quantum number $$\ell$$ or smaller parameter $$\delta$$ .

Eigensolutions and quantum fisher information for different potential models

The solutions of two potentials with one potential made up of a combination of constant, Yukawa, and inversely quadratic potentials and the other made up of constant, Coulomb, and inversely quadratic potentials are obtained under the radial Schrödinger equation using the elegant parametric Nikiforov–Uvarov method. The energy equations and their corresponding wave functions are obtained in a close and compact form. The Fisher information for configuration space and momentum space are obtained for each combination of the potentials. It has been revealed that the energy eigenvalues of each combined potential model has a turning point. It is also shown that one special case in one combined potentials and another special case in the other combined potentials have equivalent energy eigenvalues. The results for the constant potential as a subset potential in each combination are not exactly the same. The Fisher information for each combined potentials and their respective subset potentials satisfied Fisher information-based uncertainty relation. It is also shown that the effect of the screening parameter on the Fisher information at the ground state and at the first excited state for one of the combining potential has a diffused format.

Radial solution of Schrödinger equation with Hulthen-Yukawa-Inverse quadratic potential in a Point-Like defect under AB-flux field

In this paper, we determine the approximate eigenvalue solution of the non-relativistic wave equation in the presence of the Aharonov-Bohm flux field with Hulthen-Yukawa-Inverse Quadratic potential in a topological defect via point-like global monopole (PGM) geometry. We use the Greene-Aldrich improved approximation scheme into the centrifugal and reciprocal terms appear in the radial Schrödinger equation. We then solve this radial equation using the parametric Nikiforov-Uvarov method and analyze the effects on the eigenvalue solution. We see that the energy levels and the radial wave functions get modified by the topological defect of a point-like global monopole and the magnetic flux field that shows an analogue of the Aharonov-Bohm effect for the bound state. Finally, we utilize the eigenvalue solution to some potential models, such as Hulthen potential, Hulthen plus Yukawa potential, and Hulthen plus inverse quadratic potential and discuss the results.

Quantum effects with Kratzer plus generalised Yukawa potential in a point-like global monopole using different approximation schemes

In this paper, we study the quantum motions of the non-relativistic particles under the influence of the flux field in the background of a point-like global monopole with Kratzer plus generalised Yukawa potential. The solutions of the quantum system under consideration are obtained using the parametric Nikiforov–Uvarov method by employing the Greene–Aldrich approximation scheme in the centrifugal and reciprocal terms that appear in the radial equation. Afterwards, we use another approximation called the Taylor series expansion up to the first order in the exponential terms and solve the radial equation analytically using the confluent hypergeometric function. It is shown that the topological defect of a point-like global monopole influences the eigenvalue solutions of the non-relativistic particles and gets modified by this defect compared to the flat space result with this superposed potential. We also show that the energy eigenvalue of the particles depends on the quantum flux field and thus gets shifted. Finally, we compare the eigenvalue solutions obtain for these two approximations scheme used here and show graphically that the results are different in these schemes.

Relativistic energies and information entropy of the inversely quadratic Hellmann potential

The solutions to the Dirac equation are obtained in the spin and pseudospin symmetry limits are presented using the parametric Nikiforov-Uvarov (pNU) method with the inversely quadratic Hellman (IQH) potential. In the exact non-relativistic spin symmetry limit, the energy and wave function of the IQH potential are obtained and used to investigate the Shannon information entropy of the system. Numerical results of the relativistic energies of the spin and pseudospin symmetry limits of the Dirac equation with the IQH potential are presented and observed to exhibit degeneracy. Also, the results of the Shannon entropy for six states (n = 0, 1, 2, 3, 4, 5) show that the momentum space wave function and probability density are better localized than the position space wave function. Also, the Bialynicki-Birula and Mycielski (BBM) inequality is verified for the system. Our results are found to be consistent with those previously reported in the literature.

Dirac Equation for Energy-Dependent Potential With Energy-dependent Tensor Interaction

The relativistic symmetries of the Dirac equation were investigated with an energy-dependent tensor potential interaction for two different energy-dependent potentials under parametric Nikiforov-Uvarov method and supersymmetric quantum mechanics and shape-invariance method. It is observed that the energy-dependent tensor interaction has stronger removal effect of the energy degeneracies in both the spin and pseudospin symmetries than the non-energy-dependent tensor interaction.

Radial solution of Schrödinger equation with generalized inverse Hulthen and Yukawa potentials in topological defect

In this work, the generalized inverse Yukawa potential is used to explore the radial Schrödinger equation in three dimensions in a topological defect caused by a point-like global monopole. We analyze the quantum system under the influence of the quantum flux field and see that the angular quantum number l is shifted, that is, which shows an analogue to the Aharonov-Bohm effect. We use a suitable approximation scheme in the centrifugal and reciprocal terms that appear in the radial equation and solve the equation through the parametric Nikiforov-Uvarov method. Afterwards, we consider the potential of the superposition of generalized inverse Hulthen and generalized inverse Yukawa potentials in the quantum system and solve the radial equation using the same technique. The obtained eigenvalue solutions are analyzed for the topological defects of the geometry and the quantum flux and see that the results get shifted in comparison to the flat space case with these potentials.

Radial solution of Schrödinger equation with generalized inverse Hulthen and Yukawa potentials in topological defect

In this work, the generalized inverse Yukawa potential is used to explore the radial Schrödinger equation in three dimensions in a topological defect caused by a point-like global monopole. We analyze the quantum system under the influence of the quantum flux field and see that the angular quantum number l is shifted, that is, which shows an analogue to the Aharonov-Bohm effect. We use a suitable approximation scheme in the centrifugal and reciprocal terms that appear in the radial equation and solve the equation through the parametric Nikiforov-Uvarov method. Afterwards, we consider the potential of the superposition of generalized inverse Hulthen and generalized inverse Yukawa potentials in the quantum system and solve the radial equation using the same technique. The obtained eigenvalue solutions are analyzed for the topological defects of the geometry and the quantum flux and see that the results get shifted in comparison to the flat space case with these potentials.

Effects of Lorentz symmetry breaking environment on generalized relativistic quantum oscillator field

In this paper, we study the generalized Klein–Gordon oscillator under the effects of the violation of Lorentz symmetry defined by a tensor field ( KF) μναβ out of the standard model extension. We consider a possible scenario of Lorentz-violating with a Cornell-type potential form electric field and a linear magnetic field that contributes a harmonic-type central potential effects in the quantum motions of oscillator fields. The bound-state solutions of the wave equation using the parametric Nikiforov–Uvarov method by considering Coulomb- and Cornell-type potential form functions are obtained. We see that the eigenvalue solutions get modified by the Lorentz symmetry breaking effects in comparison to the Landau levels (without Lorentz-violation effects in flat space).

Hellmann potential and topological effects on non-relativistic particles confined by Aharonov–Bohm flux field

In this analysis, we investigate the quantum motions of a non-relativistic particle confined by the Aharonov–Bohm flux field with Hellmann potential (Coulomb plus Yukawa potential) in a topological defect space-time produced by a point-like defect. We employ a suitable approximation scheme in the centrifugal and reciprocal terms that appear in the radial equation and determine the eigenvalue solution using the parametric Nikiforov–Uvarov method. Afterwards, we study the quantum system with an attractive Coulomb potential and obtained the eigenvalue solution using the same NU-method. These eigenvalue solutions are analysed and see the effects of topological defects produced by a point-like defect and the AB-flux field with these potentials. We also see that in addition to the topological effects, the energy levels shift more by the magnetic flux field, which gives us an analogue of the Aharonov–Bohm effect for the bound state. Finally, we plot a few graphs of the energy levels and the radial wave function with different parameters, such as the topological defect, the magnetic flux field, and the screening parameter, and discuss the results.

Topological effects produced by point-like global monopole with Hulthen plus screened Kratzer potential on Eigenvalue solutions and NU-method

In this article, the approximate eigenvalue solution of the Schrödinger non-relativistic equation in 3D with a non-central potential of superposition of Hulthen potential and screened Kratzer potential in a point-like global monopole space-time is obtained. We employ a suitable approximation scheme like the Greene-Aldrich approximation in the centrifugal and reciprocal terms that appear in the radial equation and solve it using the parametric Nikiforov-Uvarov method. The results are analyzed for the topological defects and the magnetic flux and show that the eigenvalue solution gets modified in comparison to the flat space result with this superposed potential. Finally, we utilize the eigenvalue solution to some diatomic molecular potential models, such as screened Kratzer and Varshni potential and discuss the effects on the eigenvalue solutions.

Analytical study of gallium halides for Pὅschl-Teller potential modell

The solutions of the radial Schrödinger equation were obtained for a Pὅschl-Teller potential model using the parametric Nikiforov-Uvarov method. The non-relativistic energy and its corresponding un-normalized radial wave function for the interacting potential model were calculated explicitly. With the help of the spectroscopic constants and the calculated energy equation, the energies of gallium halides and sodium dimer were numerically obtained and compared with the observed data. The present results and the observed data showed a strong agreement. The present result revealed that the Pὅschl-Teller potential model is more fitted for the representation of sodium dimer compared to the improved Tietz potential model.

The Λ-core model for studying the binding energies of Λ-hypernuclei under pseudo-spin symmetry using the Hellmann potential

We have studied the binding energies of a group of single Λ-hypernuclei in a relativistic approach and modeled the single Λ-hypernuclei as a Λ-core binary system. Since the Hellmann potential is ideal for defining nucleon-core interaction and the single Λ-hypernuclei can be assumed as a single nucleon coupled to the whole nuclei but does not suffer from Pauli blocking, we have selected this potential for interaction between the Λ particle and the core. The time-independent Dirac equation is a reasonable option for defining the relativistic bound states that correspond to a spin-1/2 Λ hyperon in the hypernuclei. We solved this equation by using the Hellmann potential under the presence of pseudo-spin symmetry in terms of the generalized parametric Nikiforov-Uvarov method, a way to make the application of the Nikiforov-Uvarov method as plain as possible. Our results were in good agreement with experimental values and other theoretical works. Hence, this model is applicable for the Λ-hypernuclei.

Bohr Hamiltonian with inversely quadratic Yukawa plus screened Kratzer potential for triaxial nuclei

Bohr Hamiltonian with inversely quadratic Yukawa plus screened Kratzer potential for the [Formula: see text]-part and a harmonic oscillator for the [Formula: see text]-part is investigated. The expressions of energies and wave functions are obtained using the parametric Nikiforov–Uvarov method. The obtained results are used to evaluate the normalized eigen energies, the root mean square deviation and [Formula: see text] transition rates of [Formula: see text]Pt, [Formula: see text]Pt and [Formula: see text]Pt atomic nuclei. The numerical results of our model are compared to those of other relevant theoretical models and experimental data. Furthermore, to test the sensitive signature of triaxiality, we used some indicators such as the staggering effect in the [Formula: see text]-band. It appears that the results provided by our calculations are in accordance with experimental values and improved in comparison with previous models.

Investigating Some Diatomic Molecules Bounded by the Two-Dimensional Isotropic Oscillator plus Inverse Quadratic Potential in an External Magnetic Field

We investigate the nonrelativistic magnetic effect on the energy spectra, expectation values of some quantum mechanical observables, and diamagnetic susceptibility for some diatomic molecules bounded by the isotropic oscillator plus inverse quadratic potential. The energy eigenvalues and normalized wave functions are obtained via the parametric Nikiforov-Uvarov method. The expectation values square of the position r 2 , square of the momentum p 2 , kinetic energy T , and potential energy V are obtained by applying the Hellmann-Feynman theorem, and an expression for the diamagnetic susceptibility X is also derived. Using the spectroscopic data, the low rotational and low vibrational energy spectra, expectation values, and diamagnetic susceptibility X for a set of diatomic molecules (I2, H2, CO, and HCl) for arbitrary values, Larmor frequencies are calculated. The computed energy spectra, expectation values, and diamagnetic susceptibility X were found to be more influenced by the external magnetic field strength and inverse quadratic potential strength g than the vibrational frequencies and the masses of the selected molecules.