Screened Kratzer Potential Research Articles

Comment on “Thermo-magnetic properties of the screened Kratzer potential with spatially varying mass under the influence of Aharanov–Bohm (AB) and position-dependent magnetic fields”

We show that the authors of a paper published recently failed to obtain the thermodynamic properties of the system (Helmholtz free energy, entropy, internal energy, specific heat, magnetization and magnetic susceptibility). The reason is that they omitted the sum over the magnetic quantum number which is essential for the calculation of the partition function. As a consequence, their analytical expressions are unsuitable for any physical application.

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

Optical properties of spherical quantum dot using screened Kratzer potential

Here we investigate the optical properties of a spherical quantum dot using the screened Kratzer potential. The density matrix formalism is employed to study refractive index changes, along with linear and nonlinear optical absorption coefficients. To this effect, the radial Schrödinger equation is solved using the Nikiforov–Uvarov functional analysis method, resulting in analytical expressions for the energy eigenvalues and the associated eigen functions. Effects of dot size, potential parameters, and screening length on these properties are analyzed in detail for a GaAs quantum dot. The obtained results reveal that the optical response of the system is highly sensitive to the dot size and potential parameters, and thus it can be tuned accordingly. The impact of external magnetic and Aharonov–Bohm flux fields on the optical properties of the GaAs quantum dot is also discussed. The findings of this study may provide useful insights in design and optimization of quantum dot-based optoelectronic devices.

ENERGY SPECTRA, EXPECTATION VALUES, AND THERMODYNAMIC PROPERTIES OF HCl AND LiH DIATOMIC MOLECULES

The Schrödinger equation is solved by applying the Nikiforov-Uvarov-Functional Analysis method to the Hulthén plus screened Kratzer Potential. The Greene-Aldrich approximation is employed to determine the closed form expressions for the energy equation and the wave function. The Hellmann-Feynman theorem was employed to calculate the energy spectra and expectation values of various quantum states for diatomic moleculesof HCl and LiH. Subsequently, we employed the energy equation that we had previously derived to compute the partition function, which in turn enabled us to determine the thermodynamic properties associated with the diatomic molecules. The partition function for the diatomic molecules of 2Hand LiHwas calculated at different temperatures. The results indicate that the partition function of the two diatomic molecules rose as the temperature increased.The findings we obtained align with the results documented in the literature.

New bound-state solutions and statistical properties of the IMK-GIQYP and IMSK-IQYP models in 3D-NRNCPS symmetries

Within the framework of three-dimensional non-relativistic noncommutative quantum phase-space (3D-NRNCPS) symmetries, we study the three-dimensional deformed Schrödinger equation (3D-DSE) using the improved modified Kratzer plus generalized inverse quadratic Yukawa potential (IMK-GIQYP) and the improved modified screened Kratzer plus inversely quadratic Yukawa potential (IMSK-IQYP) models. For this consideration, the well-known generalized Bopp’s shifts method and standard perturbation theory are used to solve the DSE in the 3D-NRNCPS regime. For the homogeneous (H2, N2 and I2) and heterogeneous (CO, CH and NO) diatomic molecules, the new non-relativistic energy equation and eigenfunction for the IMK-GIQYP and the IMSK-IQYP models in the presence of deformation phase-space are obtained to be sensitive to the atomic quantum numbers ([Formula: see text] and m), the mixed potential depths ([Formula: see text] and V) and ([Formula: see text] and [Formula: see text]), the screening parameters ([Formula: see text] and [Formula: see text]), and non-commutativity parameters ([Formula: see text] and [Formula: see text]) for the IMK-GIQYP and the IMSK-IQYP, respectively. We investigate the newly obtained bound state eigenvalues of the DSE in 3D-NRNCPS symmetries using the IMK-GIQYP and the IMSK-IQYP, with appropriate adjustments made to the improved modified Kratzer potential, improved modified screened Kratzer potential, improved generalized inverse quadratic Yukawa potential model and improved inversely quadratic Yukawa potential model. Additionally, in 3D-NRNCPS symmetries, the thermal properties of the IMK-GIQYP and the IMSK-IQYP, including their partition function, mean energy, free energy, specific heat and entropy, are thoroughly examined. Significant areas, including atomic and molecular physics, find many uses for this study.

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.

New relativistic and non-relativistic investigation of deformed Klein–Gordon and Schrödinger equations for new improved screened Kratzer potential in the framework of non-commutative space

The deformed Klein–Gordon equation has been solved in three-dimensional extended relativistic quantum mechanics (3D-ERQM) symmetries for the newly improved screened Kratzer potential (NISKP) model under the influence of the deformation space–space symmetries. The new relativistic energy eigenvalues were calculated using the parametric Bopp’s shift method and standard perturbation theory in addition to the approximation scheme suggested by Greene and Aldrich for the inverse square terms. The new relativistic energy eigenvalues of (LiH, HCl, CO and H2) molecules under the NISKP model were shown to be sensitive to the atomic quantum numbers ([Formula: see text]), mixed potential depths ([Formula: see text]), the screening parameter’s inverse [Formula: see text], control parameter [Formula: see text] and non-commutativity parameters ([Formula: see text], [Formula: see text], [Formula: see text]). In addition, we analyzed the non-relativistic energy values by applying the well-known transmission rules known in the literature. Furthermore, we studied many special cases useful to researchers in the framework of the new extended symmetries, such as the new screened cosine Kratzer potential, the new screened Kratzer potential (SKP), the new Kratzer potential, the new coshine Yukawa potential, the new coshine Yukawa potential, the new shifted improved SKP and the new shifted SKP. The study is further extended to calculate the mass spectra of mesons of the heavy quarkonium system such as charmonium [Formula: see text], bottomonium [Formula: see text], [Formula: see text] and light mesons [Formula: see text] and [Formula: see text] that have the quark and antiquark flavor within the framework of the NISKP model in 3D-ENRQM symmetries.

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.

Conformable fractional study of nuclear energy excitation by Bohr Hamiltonian with screened Kratzer potential for triaxial nuclei

In this work, we obtain new solutions of the Bohr Hamiltonian model appropriate for triaxial nuclei, with screened Kratzer potential in the framework of conformable fractional derivative. The analytical solutions for energy spectra are obtained using the conformable fractional Nikiforov–Uvarov method. We discuss the link between the present model and other relevant related models such as Z(5) model, classical screened Kratzer model and conformable fractional Kratzer model. The effect of the fractional-order parameter is investigated on the variations of the interaction potential. The normalized eigen-energies are calculated as well as normalized B(E2) transitions probabilities at different values of the fractional-order parameter. Our results reproduced well the experimental data for [Formula: see text]Xe, [Formula: see text]Xe, [Formula: see text]Xe, [Formula: see text]Pt, [Formula: see text]Pt and [Formula: see text]Pt atomic nuclei, and are found to be improved in comparison with other related theoretical models.

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.

The Study of Electronic States of Ni and ScI Molecules with Screened Kratzer Potential

In this study, the analytical solutions of the Schrödinger equation with the screened Kratzer potential model is solved using the well-known Nikiforov-Uvarov method. The energy spectrum and the normalized wave function with the Greene-Aldrich approximation to the centrifugal term are obtained. The energy spectrum is used to generate eigenvalues for X3Σ- state of NI and X1Σ+ state of ScI molecules respectively. The calculated results agree excellently with the experimental data. This research finds application in chemistry, industry, molecular physics and studies on magnetocaloric effect for several molecules. Our findings also demonstrate that the approximation scheme is well suited for this potential.

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

By employing the extended Nikiforov–Uvarov (ENU) method, we solved the radial Schrodinger equation with the shifted screened Kratzer potential model. The analytical expression of the energy eigenvalues and numerical results were determined for some selected diatomic molecule systems. Variations of the energy eigenvalues obtained with potential parameters and quantum numbers were discussed graphically. Also, variations of different thermodynamic properties with temperature and maximum vibration quantum numbers were discussed extensively. Our results correspond to the results obtained in the literatures. The shifting parameters contribute a great effect to the energy results obtained. It has also been established that there exists a critical temperature at specific entropy values for the selected diatomic molecule systems.

Optical Second Harmonic Generation in GaAs/Ga1−xAlxAs Quantum Dots with Screened Kratzer Potential

Herein, the second harmonic generation (SHG) associated with intersubband transitions in semiconductor quantum dots (QDs) is studied theoretically, with emphasis on the effects of the screened Kratzer (SK) potential parameters and regulating factors, such as temperature and the depth of potential. The Nikiforov–Uvarov Functional Analysis (NUFA) method is applied for solving the radial Schrödinger equation. Then, the formulae for the SHG coefficient are derived using the compact‐density‐matrix method. The results display that the SK potential parameters and the regulating factors play a key role in both the peak and position changes of the SHG in semiconductor QDs system.

Bohr Hamiltonian with Hulthen plus screened Kratzer potential using super symmetric quantum mechanics

In this paper, we look for a novel analytical solution of the Bohr Hamiltonian in the presence of the Hulthen plus screened Kratzer potential in [Formula: see text]-part of the collective nuclear potential. The new expression for the energy spectra is obtained using the method of super symmetric quantum mechanics. The effect of the Hulthen plus screened Kratzer potential is studied on root mean square deviation, and normalized eigen energies of ground state band, [Formula: see text]-band and [Formula: see text]-band of 192Pt, 194Pt and 196Pt atomic nuclei. The [Formula: see text] transition rates are calculated for the latter potential. Furthermore, our results are compared with experimental data, and other relevant theoretical works. We discuss on how the combination of these two potentials makes it possible to improve the results of energy spectra and quadrupole transitions of triaxial nuclei. We discuss the quantitative and qualitative descriptions concerning the structure of the nucleus using some indicators such as root mean square and staggering of the [Formula: see text]-band. The results provided by our model are found to be in good agreement with experimental data and improved in comparison with previous works.

Approximate solutions of the Schrödinger equation with Hulthén plus screened Kratzer Potential using the Nikiforov–Uvarov – functional analysis (NUFA) method: an application to diatomic molecules

The Schrödinger equation was solved for the Hulthén plus screened Kratzer Potential (HSKP) via the Nikiforov–Uvarov – functional analysis (NUFA) method. The bound-state energy and wave function for the HSKP were obtained in a closed form by applying the Greene–Aldrich approximation scheme to the inverse-square term. Using the resulting energy equation, we computed the energy spectra for 12 diatomic molecules (CuLi, TiH, VH, TiC, HCl, LiH, H2, ScH, CO, I2, N2, and NO) for various quantum states. To show the accuracy of our procedure, four special cases of the collective potential were obtained, and the results are in excellent agreement with the existing literature.

Aharonov–Bohm (AB) flux and thermomagnetic properties of Hellmann plus screened Kratzer potential as applied to diatomic molecules using Nikiforov–Uvarov-Functional-Analysis (NUFA) method

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.

Bohr Hamiltonian of triaxial nuclei using Morse plus screened Kratzer potentials with the extended Nikiforov–Uvarov method

In this work, Bohr Hamiltonian is used to explain the behavior of triaxial nuclei. A new potential, called Morse plus screened Kratzer potential, has been developed for the [Formula: see text]-part with [Formula: see text] fixed at [Formula: see text]. The Extended Nikiforov–Uvarov method involving Confluent Heun functions is used to derive the wave function and energy expression. The electric quadrupole transition rates and energy spectrum of platinum [Formula: see text] are determined and compared with the experimental data and some theoretical results.

Thermo-magnetic properties of the screened Kratzer potential with spatially varying mass under the influence of Aharanov-Bohm(AB) and position-dependent magnetic fields

In this study, the solution of the position-dependent mass Schrödinger equation (PDMSE) for the screened Kratzer potential with the Aharanov-Bohm and position-dependent external magnetic fields are investigated using asymptotic iteration method. The energy eigenvalues and the corresponding eigenfunctions are obtained in closed form. We evaluated the partition function of the system and calculated the thermodynamic properties of the system such as Helmholtz free energy, entropy, internal energy, specific heat and the magnetization and magnetic susceptibility of the system at zero and finite temperatures. • The position-dependent mass Schrödinger equation (PDMSE) for the screened Kratzer potential with the (AB)and position-dependent external magnetic fields are investigated using asymptotic iteration are investigated. • The energy eigenvalues and the corresponding eigenfunctions are calculated. • The partition function, Helmholtz free energy, entropy, are evaluated. • And the magnetization and susceptibility of the system are also calculated.

Bound states and scattering phase shift of relativistic spinless particles with screened Kratzer potential

The bound and scattering states of relativistic spinless particles with screened Kratzer potential were investigated using the modified factorization method. We employed the Greene–Aldrich approximation scheme and a coordinate transformation to obtain the approximate bound state energy eigenvalues in terms of the hypergeometric function, bound state eigenfunction, scattering state energy relation and scattering phase shift, respectively. The analytical and numerical results were presented. The effects of the potential parameters on the bound state energy eigenvalues and the scattering phase shift were discussed extensively and graphically. Our results promise to be very relevant in many areas of theoretical physics, chemistry, mathematics and engineering.

Klein–Gordon Equation and Nonrelativistic Thermodynamic Properties with Improved Screened Kratzer Potential

By employing the concept of the newly proposed Nikiforov-Uvarov functional analysis (NUFA) method, we solved the Klein–Gordon equation with the improved screened Kratzer potential (ISKP) model. The analytical expressions of the energy eigensolutions and numerical results were obtained for different diatomic molecules, both at the relativistic and nonrelativistic limits. Variation of the energy eigenvalues with potential parameters and quantum numbers was also discussed. In addition, the effects of temperature and upper bound vibration quantum number on the vibrational partition function and other thermodynamic functions have been discussed. Different special cases have been obtained from the ISKP, which correspond to the results in literatures. It was observed that the control parameter of ISKP has a great effect on the energy eigenvalues obtained.