Improved energy equations and thermal functions for diatomic molecules: a generalized fractional derivative approach.

Context: This work presents analytical expressions for ro-vibrational energy models of diatomic molecules by introducing fractional parameters to improve molecular interaction analysis. Thermodynamic models, including Helmholtz free energy, mean thermal energy, entropy, and isochoric heat capacity, are formulated for diatomic molecules such as CO (X ∑), Cs (3 ∑), K (X ∑), Li (6 Π), Li (1 Δ), Na (5 Δ), Na (C(2) Π), and NaK (c ∑). The incorporation of fractional parameters improves predictive accuracy for vibrational energies, as shown by reductions in percentage average absolute deviations from 0.

Relativistic bound state solutions and quantum information theory in D dimensions under exponential-type plus Yukawa potentials.

The bound-state solution of the radial Klein-Gordon equation has been obtained under the interaction of an exponential-type and Yukawa potential functions. The Greene-Aldrich approximation has been used to overcome the centrifugal barrier and enable the analytical solutions of the energy and wave functions in closed form. The momentum space wave function in D dimensions has been constructed using the Fourier transform.

Examining the quantum fisher information in the interaction of a dirac system with a squeezed generalized amplitude damping channel.

The inherent association between real quantum systems and their surrounding environment invariably results in decoherence, leading to the loss of entanglement. This diminution in entanglement coincides with a decline in the fidelity of transmitted information using the entangled quantum resource. This study scrutinizes the impact of the squeezed generalized amplitude damping (SGAD) channel on quantum Fisher information (QFI) parameters.

Approximate solutions of the spin and pseudospin symmetries under coshine Yukawa tensor interaction.

The approximate solutions of the Dirac equation for spin symmetry and pseudospin symmetry are studied with a coshine Yukawa potential model via the traditional supersymmetric approach (SUSY). To remove the degeneracies in both the spin and pseudospin symmetries, a coshine Yukawa tensor potential is proposed and applied to both the spin symmetry and the pseudospin symmetry. The proposed coshine tensor potential removes the energy degenerate doublets in both the spin symmetry and pseudospin symmetry for a very small value of the tensor strength (H = 0.

Non-relativistic energy equations for diatomic molecules constrained in a deformed hyperbolic potential function.

Context: In this paper, the approximate analytical energy equations for the deformed hyperbolic potential have been obtained for arbitrary parameters of the potential. The potential function was transformed to a molecular potential by subjecting it to the Varshni conditions which allows for the determination of the energy levels of diatomic molecules. The molecular vibrational energy spectra for [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text] diatomic molecules were obtained and found to match with the results obtained with another analytical approach, potential functions, and experimental data.

Bound-state energy spectrum and thermochemical functions of the deformed Schiöberg oscillator.

In this study, a diatomic molecule interacting potential such as the deformed Schiöberg oscillator (DSO) have been applied to diatomic systems. By solving the Schrödinger equation with the DSO, analytical equations for energy eigenvalues, molar entropy, molar enthalpy, molar Gibbs free energy and constant pressure molar heat capacity are obtained. The obtained equations were used to analyze the physical properties of diatomic molecules.

Energy eigenvalues and finite-temperature magnetization for the improved Scarf II potential in the presence of external magnetic and Aharonov-Bohm flux fields.

In this paper, the bound state solutions of the radial Schrödinger equation are obtained in closed form under an improved Scarf II potential energy function (ISPEF) constrained by external magnetic and Aharonov-Bohm (AB) flux fields. By constructing a suitable Pekeris-like approximation scheme for the centrifugal barrier, approximate analytical expressions for the bound-states and thermal partition function were obtained. With the aid of the partition function, an explicit equation for magnetization at finite temperatures is developed.

Information theory and thermodynamic properties of diatomic molecules using molecular potential.

Owing to the devise applications of molecules in industries, the bound state solution of the non-relativistic wave equation with a molecular potential function has been obtained in a closed-form using the Nikiforov-Uvarov method. The solutions of the bound state are then applied to study the information-theoretic measures such as the one-dimensional Shannon and Renyi entropic densities. The expectation values for the position and momentum spaces were obtained to verify the Heisenberg's uncertainty principle.

Thermomagnetic properties and its effects on Fisher entropy with Schioberg plus Manning-Rosen potential (SPMRP) using Nikiforov-Uvarov functional analysis (NUFA) and supersymmetric quantum mechanics (SUSYQM) methods.

Thermomagnetic properties, and its effects on Fisher information entropy with Schioberg plus Manning-Rosen potential are studied using NUFA and SUSYQM methods in the presence of the Greene-Aldrich approximation scheme to the centrifugal term. The wave function obtained was used to study Fisher information both in position and momentum spaces for different quantum states by the gamma function and digamma polynomials. The energy equation obtained in a closed form was used to deduce numerical energy spectra, partition function, and other thermomagnetic properties.

Analytical solutions and Herzberg's energy level for modified shifted morse molecular system.

The solution of the radial Schrödinger equation for the modified shifted Morse potential model is obtained using an approximate supersymmetric approach. The two different formulae for the computation of the centrifugal distortion constant are clearly examined to deduce the formula that gives the result that perfectly aligns with the experimental data. Numerical values for different molecules are computed for the two different values of the centrifugal distortion constant (dissociation energy) obtained from two different equations.

Theoretic measure and thermal properties of a standard Morse potential model.

Since the proposition of the standard form of Morse potential [Formula: see text] model over the years, there has not been much attention on the potential. Its application to different studies such as the thermodynamic properties and information theory are yet to be reported to the best of our understanding. In this study, the solutions of the radial Schrödinger equation for the standard Morse potential is obtained using supersymmetric approach.

Eigen-solutions and thermal properties of multi-parameter exponential potential.

In this work, we determined an approximate eigen solutions of Modified multi-parameter exponential potential using supersymmetric quantum mechanics approach (SUSY) with improved Greene-Aldrich approximation to the centrifugal term. The energy equation and its corresponding normalised radial wave function were fully obtained. The proposed potential reduces to other useful potentials like Rosen-Morse, Hellmann, Yukawa and Coulomb potential as special cases.

Non-relativistic molecular modified shifted Morse potential system.

A shifted Morse potential model is modified to fit the study of the vibrational energies of some molecules. Using a traditional technique/methodology, the vibrational energy and the un-normalized radial wave functions were calculated for the modified shifted Morse potential model. The condition that fits the modified potential for molecular description were deduced together with the expression for the screening parameter.

Relationship between Parents' Physical Activity Level and the Motor Development Level and BMI of Their Children.

All the variables that arise in family dynamics can have significant effects on the lives of children concerning their nutritional status and motor development. The objective of this study was to relate the PAL of parents to the level of motor development and the BMI of their children. A total of 198 subjects participated, with the age of the students ranging between 8 and 10 years.

Context-dependent roles of cellular senescence in normal, aged, and disease states.

Cellular senescence is a state of irreversible cell cycle arrest that often emerges after tissue damage and in age-related diseases. Through the production of a multicomponent secretory phenotype (SASP), senescent cells can impact the regeneration and function of tissues. However, the effects of senescent cells and their SASP are very heterogeneous and depend on the tissue environment and type as well as the duration of injury, the degree of persistence of senescent cells and the organism's age.

All About (NK Cell-Mediated) Death in Two Acts and an Unexpected Encore: Initiation, Execution and Activation of Adaptive Immunity.

NK cells are key mediators of immune cell-mediated cytotoxicity toward infected and transformed cells, being one of the main executors of cell death in the immune system. NK cells recognize target cells through an array of inhibitory and activating receptors for endogenous or exogenous pathogen-derived ligands, which together with adhesion molecules form a structure known as immunological synapse that regulates NK cell effector functions. The main and best characterized mechanisms involved in NK cell-mediated cytotoxicity are the granule exocytosis pathway (perforin/granzymes) and the expression of death ligands.

Vibrational energies of some diatomic molecules for a modified and deformed potential.

A molecular potential model is proposed and the solutions of the radial Schrӧdinger equation in the presence of the proposed potential is obtained. The energy equation and its corresponding radial wave function are calculated using the powerful parametric Nikiforov-Uvarov method. The energies of cesium dimer for different quantum states were numerically obtained for both negative and positive values of the deformed and adjustable parameters.

Solutions of the Schrödinger equation and thermodynamic properties of a combined potential.

The solution of the radial Schrödinger equation was obtained using the methodology of supersymmetric approach with a combination of modified generalized Pöschl-Teller potential and inversely quadratic Yukawa potential model. The non-relativistic ro-vibrational energy spectra and the corresponding wave functions were obtained and numerical results were generated for some states. The variation of energy of the combined potential and the subsets potentials with the screening parameter for various quantum number were graphically studied.

Ro-vibrational energies of cesium dimer and lithium dimer with molecular attractive potential.

An approximate solution of the Schrӧdinger equation for a molecular attractive potential was obtained using the parametric Nikiforov-Uvarov method. The energy equation and the corresponding radial wave functions were calculated. The effects of the potential parameters on the energy eigenvalues were examined.

Bound-state solutions and thermal properties of the modified Tietz-Hua potential.

An approximate solutions of the radial Schrödinger equation was obtained under a modified Tietz-Hua potential via supersymmetric approach. The effect of the modified parameter and optimization parameter respectively on energy eigenvalues were graphically and numerically examined. The comparison of the energy eigenvalues of modified Tietz-Hua potential and the actual Tietz-Hua potential were examined.

Spin and pseudospin solutions to Dirac equation and its thermodynamic properties using hyperbolic Hulthen plus hyperbolic exponential inversely quadratic potential.

In this research article, the modified approximation to the centrifugal barrier term is applied to solve an approximate bound state solutions of Dirac equation for spin and pseudospin symmetries with hyperbolic Hulthen plus hyperbolic exponential inversely quadratic potential using parametric Nikiforov-Uvarov method. The energy eigen equation and the unnormalised wave function were presented in closed and compact form. The nonrelativistic energy equation was obtain by applying nonrelativistic limit to the relativistic spin energy eigen equation.

Eigensolution techniques, expectation values and Fisher information of Wei potential function.

An approximate solution of the one-dimensional relativistic Klein-Gordon equation was obtained under the interaction of an improved expression for Wei potential energy function. The solution of the non-relativistic Schrödinger equation was obtained from the solution of the relativistic Klein-Gordon equation by certain mappings. We have calculated Fisher information for position space and momentum space via the computation of expectation values.

Analytical determination of theoretic quantities for multiple potential.

The approximate analytical solutions of the three-dimensional radial Schrödinger wave equation with a multiple potential function has been studied using a suitable approximation scheme to the centrifugal term in the framework of parametric Nikiforov-Uvarov method. The energy equation and the wave function were obtained. The calculated wave function was used to study Shannon entropy and variance via expectation values.

Application of Schrödinger equation in quantum well of CuZnSnS quaternary semiconductor alloy.

An approximate solution of the radial Schrödinger equation is obtained with a generalized group of potentials in the presence of both magnetic field and potential effect using supersymmetric quantum mechanics and shape invariance methodology. The energy bandgap of the generalized group of potentials was calculated for wave cases at the ground state. By varying the numerical values of the potential strengths, the energy band gap of Hellmann's potential and Coulomb-Hulthẻn potential respectively were obtained.

Bound state solutions of the Schrödinger equation and its application to some diatomic molecules.

We apply the supersymmetric quantum mechanics and shape invariance approach to obtain the solutions of the 3-dimensional Schrödinger equation in the presence of a newly proposed potential model called hyperbolic-sinus potential function for any ℓ-state. Rotational-vibrational energy eigenvalues of some diatomic molecules are numerically calculated. Special cases of interest of the hyperbolic-sinus potential function are also studied.