Kratzer Potential Research Articles

Effect of position-dependent mass formalism on expectation values and thermodynamic properties of some molecules with Kratzer potential

Effect of position-dependent mass formalism on expectation values and thermodynamic properties of some molecules with Kratzer potential

Shannon information entropy with improved Kratzer potential under the effects of magnetic and Aharonov-Bohm flux fields

Shannon information entropy with improved Kratzer potential under the effects of magnetic and Aharonov-Bohm flux fields

Path integral solution for a Dirac particle in a Generalized Inverse Quadratic Yukawa potential

In this work, the analytical solutions of the Dirac equation with the spin and pseudospin symmetry for the Generalized Inverse Quadratic Yukawa (GIQY) potential have been investigated. The problem was approximately addressed using path integral formalism. We present the energy eigenvalues expression along with the upper and lower radial wave functions for any given k-state. The Schrödinger solutions for the GIQY potential and Dirac’s solutions for Kratzer potential, Yukawa potential, inversely quadratic Yukawa potential, and Coulomb potential have also been calculated and compared to results from previous investigations.

Approximate solutions for diatomic molecules under combined potentials in a global monopole and Aharonov–Bohm flux field

AbstractBound state energy eigensolutions of nine different diatomic molecules, specifically, , TiH, , CO, NO, ScH, CrH, HCl and LiH, placed in a point‐like global monopole, have been calculated by solving the time‐independent Schrödinger equation (SE). The molecules are confined by the Aharonov–Bohm (AB) flux field and the interaction potential among the charged particles is governed by the combined screened modified Kratzer potential (SMKP) plus Hulthén potential model. Three other special cases of the interaction potential have also been discussed here. Asymptotic iteration method has been used for the mathematical calculations. It is difficult to solve the SE exactly for any non‐zero values of the azimuthal quantum number due to the presence of the centrifugal barrier term. The well‐known Pekeris approximation technique for the terms and has taken into consideration for the purpose of performing numerical computations connected to an arbitrary state. The outcomes of this study are in reasonable agreement with the results of previous research on SMKP, Kratzer‐Fues potential, and modified Kratzer potential in the Minkowski space. It is observed that the energy spectra of the diatomic molecules suffer considerable change due to the effects of the background AB‐flux field and topological defect parameter.

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.

The Nonlinear Optical Properties of Self-Assembled InAs/GaAs Quantum Dot: Effect of Hydrostatic Pressure and Temperature

In this study, we have investigated the effects of temperature (T) and hydrostatic pressure (P) on both the nonlinear and linear optical properties of an InAs/GaAs core/shell quantum dot (QD) system with a Screened-Modified Kratzer potential (SMKP). To achieve this objective, we calculated the energy levels and their corresponding wave functions of the structure using the diagonalization method within the framework of the effective mass approximation. Analytical expressions for the absorption coefficients (ACs) and relative refractive index changes (RRICs) were derived using the compact-density-matrix approach. In our numerical calculations, we first determined the variation of the SMKP dependence, the dipole transition matrix element, and the electron energies of the ground (1s) and first excited state (1p) over a range of hydrostatic pressure (P) and temperature (T). As a result, the obtained numerical calculations revealed that changes in P and T influence both the magnitude and position of the resonant peaks that define the ACs and RRICs

Fisher Information for a System Composed of a Combination of Similar Potential Models

The solutions to the radial Schrödinger equation for a pseudoharmonic potential and Kratzer potential have been studied separately in the past. Despite different reports on the Kratzer potential, the fundamental theoretical quantities such as Fisher information have not been reported. In this study, we obtain the solution to the radial Schrödinger equation for the combination of the pseudoharmonic and Kratzer potentials in the presence of a constant-dependent potential, utilizing the concepts and formalism of the supersymmetric and shape invariance approach. The position expectation value and momentum expectation value are calculated employing the Hellmann–Feynman Theory. These expectation values are then used to calculate the Fisher information for both position and momentum spaces in both the absence and presence of the constant-dependent potential. The results obtained revealed that the presence of the constant-dependent potential leads to an increase in the energy eigenvalue, as well as in the position and momentum expectation values. Additionally, the constant-dependent potential increases the Fisher information for both position and momentum spaces. Furthermore, the product of the position expectation value and the momentum expectation value, along with the product of the Fisher information, satisfies both Fisher’s inequality and Cramer–Rao’s inequality.

Solutions of the Schrödinger equation with velocity-dependent potentials:a study on Kratzer, Mie and Hulthen potentials

The effect of isotropic velocity-dependent potentials on the bound state energy eigenvalues of the Kratzer, Mie and Hulthen potentials is obtained for any quantum states in the presence of constant form factor εr=γρ0. The corresponding energy eigenvalues and eigenfunctions are determined and tabulated for a set of finite quantum numbers n and l in the framework of the well-known 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

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

Nonlinear optical properties of tunable spherical quantum dots under like-screened Kratzer potential

Using the effective mass approximation and the iterative procedure, we study the optical rectification (OR) coefficient of a spherical quantum dot (QD) system with like-screened Kratzer potential (LSKP), taking into account the influence of the confinement potential depth, quantum size and external environment. Our results show that the magnitude of the OR coefficient is strongly dependent on the magnitude of the tunable factor, whose peak value will be red-shifted or blue-shifted. Interestingly, the limiting potential depth and temperature have opposite effects on the OR coefficient in terms of peak location and size. Therefore, it is necessary to pay more attention to the influence of internal and external parameters on nonlinear optical effects, and apply the theory to practical experiments and the manufacture of optoelectronic devices.

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.

Energy spectrum of some diatomic molecules using Nikiforov-Uvarov functional analysis

In this present work, the Nikiforov-Uvarov functional analysis is suggested to determine the solutions of the Schrodinger equation supported by different types of potentials and employing the Greene-Aldrich approximation. The objective was to estimate the energy spectrum of some diatomic molecules (CO, NO, N2, CH) by resolving the Schrodinger equation with the collective potential model (modified Kratzer potential plus Yukawa potential). As we compared our eigenvalue outcomes with other numerical results that were acquired by other researchers for the specific case of modified Kratzer potential, we observed that this method produced satisfactory results. The present approach may be applied to similar problems in the literature.

New Eigensolution of the Klein--Gordon and Shrödinger equations for improved modified Yukawa-Kratzer potential and its applications using Boop's Shift method and standard perturbation theory in the 3D-ERQM and 3D-ENRQM symmetries

The deformed Klein-Gordonequation has been solved in three-dimensional extended relativistic quantum mechanics (3D-ERQM) symmetries for the improved modified Yukawa-Kratzer potential (IMYKP) 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 IMYKP model it was shown to be sensitive to the atomic quantum numbers (j, l, s, m), mixed potential depths (V0, De, re), the screening parameter’s inverse α and noncommutativity parameters (Θ,τ ,χ). In addition, we analyzed the nonrelativistic energy values by applying the well-known transmission rules known in the literature. In addition, we studied many special cases useful to researchers in the framework of the new extended symmetries, such as the improved modified Kratzer potential, the improved generalized Kratzer potential, the improved Kratzer potential, the improved modified Kratzer plus screened Coulomb potential, the improved Hellmann potential, the improved Yukawa potential, and improved inversely square Yukawa potential. We noticed that these particular results are identical to our previous work and other known works in the literature. The study is further extended to calculate the mass spectra of mesons of charmonium (cc) and bottomonium (bb) within the framework of the IMYKP model in three-dimensional extended non-relativistic quantum mechanics (3D-ENRQM) symmetries.

Path integral treatment of a Klein Gordon particle with generalized inverse Quadratic Yukawa potential

We solved the Klein–Gordon equation for a generalized inverse quadratic Yukawa (GIQY) potential via path integrals approach. We applied approximations to deal with the terms 1/r 2 and 1/r. A path integral representation of Green’s function relating to a particle moving in a mixture of equal vector and scalar potentials was established. To integrate Green’s function, a space-time transformation was successfully used, and the present problem was reduced to a previously known modified Pöschl-Teller potential problem. The integrated Green’s function contains important information about the considered system, from which we obtained energy eigenvalues and the corresponding normalized eigenfunctions for various values of n and ℓquantum numbers. Numerical results, Schrödinger solutions, and special cases such as the modified screened Coulomb plus inversely quadratic Yukawa potential, Kratzer potential, Yukawa potential, and Coulomb potential were also considered. These results are largely consistent with previous studies.

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.

Lattice sum for a hexagonal close-packed structure and its dependence on the c/a ratio of the hexagonal cell parameters.

We continue the work by Lennard-Jones and Ingham, and later by Kane and Goeppert-Mayer, and present a general lattice sum formula for the hexagonal close packed (hcp) structure with different c/a ratios for the two lattice parameters a and c of the hexagonal unit cell. The lattice sum is expressed in terms of fast converging series of Bessel functions. This allows us to analytically examine the behavior of a Lennard-Jones potential as a function of the c/a ratio. In contrast to the hard-sphere model, where we have the ideal ratio of c/a=sqrt[8/3] with 12 kissing spheres around a central atom, we observe the occurrence of a slight symmetry-breaking effect and the appearance of a second metastable minimum for the (12,6) Lennard-Jones potential around the ratio c/a=2/3. We also show that the analytical continuation of the (n,m) Lennard-Jones potential to the domain n,m<3 such as the Kratzer potential (n=2,m=1) gives unphysical results.

New bound state solutions of diatomic molecules and mass spectrum of heavy quarkonium with improved modified Kratzer potential plus screened Coulomb potential model in the framework of three-dimensional nonrelativistic noncommutative phase-space symmetries

Approximate analytical solutions of the modified Schrodinger equation have been obtained with a combination of two proposed potentials, called the improved modified Kratzer potential plus screened Coulomb (IMKSC) potential, using the approximation scheme to the centrifugal term for any l-states. We applied the generalized Bopp’s shift method and standard perturbation theory. IMKSC is a superposition of modified Kratzer potential plus screened Coulomb (MKSC) potential, and new terms appear as a result of the effects of the noncommutativity properties of space and phase potential on the MKSC potential. The new bound state energy eigenvalues for some diatomic molecules were obtained in terms of the discrete atomic quantum numbers (j,n,s,m), the infinitesimal NC phase-space parameters, the dissociation energy, the equilibrium internuclear separation, the depth of the potential, and the range of the potential. Furthermore, we have shown that the NC-Hamiltonian operator is the sum of the Hamiltonian operator of the MKSC potential, the perturbed spin-orbit, and the modified Zeeman operator. The new mass spectra of heavy quarkonium systems are calculated using the new energy spectrum expression. It appears as a combination of corresponding values in the literature plus an infinitesimal part that describes the deformation phase-space.