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 = 0.05). This shows that the coshine Yukawa tensor is more effective than the real Yukawa tensor. The non-relativistic limit of the spin symmetry is obtained by using certain transformations. The results obtained showed that the coshine Yukawa potential and the real Yukawa potential has the same variation with the angular momentum number but the variation of the screening parameter with the energy for the two potential models differs. However, the energy eigenvalues of the coshine Yukawa potential model, are more bounded compared to the energies of the real Yukawa potential model.

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. Utilizing the energy spectrum equation, the thermodynamic vibrational partition function is obtained via the Poisson summation. Other thermodynamic function variations with absolute temperature have been obtained numerically for four diatomic molecules (H2, N2, O2, and HF) using Maple 18 software. The Shannon global entropic sum inequality has also been verified. The Renyi sum for constrained index parameters satisfies the global entropic inequality. The thermodynamic properties of the four molecules are similar and conform to works reported in the existing literature. The obtained vibrational energies are in fair agreement with the ones obtained using other forms of potential energy. The result further indicates that the lowest bounds for the Shannon, Renyi, and Heisenberg inequalities are ground states phenomena.

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. The results show that with an application of AB and magnetic fields, the numerical energy eigenvalues for different magnetic quantum spins decrease as the quantum state increases and completely removes the degeneracy of the energy spectra. Also, the numerical computation of Fisher information satisfies Fisher information inequality products, indicating that the particles are more localized in the presence of external fields than in their absence, and the trend shows complete localization of quantum mechanical particles in all quantum states. Our potential reduces to Schioberg and Manning-Rosen potentials as special cases. Our potential reduces to Schioberg and Manning-Rosen potentials as special cases. The energy equations obtained from the NUFA and SUSYQM were the same, demonstrating a high level of mathematical precision.

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. The ground state energy spectra for different molecules are obtained using Herzberg's energy level equation as a standard for some molecules. The results of the modified shifted Morse potential are compared with the results from Herzberg's energy level equation and the experimental data. Our study reveals that the results for one of the two centrifugal distortion constants are closer to the standard results and the experimental data in all the molecules studied.

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. The effect of the quantum number on the energy eigenvalue for the standard Morse potential is examined numerically for the hydrogen molecule (H2), lithium molecule (Li2), and potassium molecule (K2). Using the energy equation and the wave function obtained, the theoretic measures and thermodynamic properties of hydrogen, lithium, and potassium molecules are calculated via maple program. It has been shown that the energy of the standard Morse potential is fully bounded for the three molecules studied. A higher concentration of electron density corresponds to a strongly localized distribution in the position configuration. The Beckner, Bialynicki-Birula, and Mycieslki (BBM) inequality is satisfied for both the ground state and the first excited state. Finally, the product of uncertainty obtained obeyed the Heisenberg uncertainty relation.

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. The thermodynamic properties like the vibrational mean energy ( U ß , V ), Vibrational heat capacity ( C ß , V ), vibrational entropy ( S ß , V ) and vibrational free energy ( F ß , V ) of the interacting potential were studied via partition function ( Z ß , V ) obtained from the resulting energy equation. This study was applied to three diatomic molecules: Chromium hydride (CrH), Titanium Hydride (TiH) and Thiocynate (ScN). To ascertain the high degree of our analytical mathematical accuracy, we compared the results of special cases with an existing results. These were found to be in excellent agreement with the existing results.

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. The vibrational energies of SiC, NbO, CP, PH, SiF, NH and Cs2 molecules were computed by inserting their respective spectroscopic constants into the calculated energy equation. It was shown that the calculated results for all the molecules agreement perfectly with the experimental RKR values. The present potential performs better than Improved Morse and Morse potentials for cesium dimer. Finally, the real Morse potential model was obtained as a special case of the modified shifted potential.

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

A molecular potential model is proposed and the solutions of the radial SchrÓ§dinger 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. The results for sodium dimer and lithium dimer were calculated numerically using their respective spectroscopic parameters. The calculated values for the three molecules are in excellent agreement with the observed values. Finally, we calculated different expectation values and examined the effects of the deformed and adjustable parameters on the expectation values.

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

An approximate solution of the SchrÓ§dinger 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. The thermal properties under the molecular attractive potential were calculated and the behaviour of the thermal properties with the maximum quantum state (λ) and the temperature parameter (ß) respectively, were studied. Using the molecular spectroscopic parameters, the Rydberg-Klein-Rees (RKR) of cesium dimer and lithium dimer were both obtained and compared with the experimental values. The RKR values of both cesium dimer and lithium dimer calculated aligned with the observed values. The deviation and average deviation of the RKR for each molecule were also calculated.

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. The ro-vibrational energy of four molecules were also presented numerically. The thermal properties of the modified Tietz-Hua potential were calculated and the effect of temperature on each of the thermal property were examined under hydrogen fluoride, hydrogen molecule and carbon (ii) oxide. The study reveals that for a very small value of the modified parameter, the energy eigenvalues of the modified Tietz-Hua potential and that of the actual Tietz-Hua potential are equivalent. Finally, the vibrational energies for Cesium molecule was calculated and compared with the observed value. The calculated results were found to be in good agreement with the observed value.