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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 Schr¨odinger 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. [ABSTRACT FROM AUTHOR]

In this work, we find the exact solution of Schrödinger wave equation for position-dependent mass with pseudoharmonic oscillator using extended Nikiforov–Uvarov method. We obtained the energy eigen equation presented in a closed and compact form and used the result to study both superstatistics and thermodynamic properties by first determining the partition function of the system. The unnormalized wave function was obtained and expressed in terms of confluent Heun function. Using the resulting energy eigen equation, the numerical computation was computed for varying masses with fixed physical constant potential parameter λ . The numerical result shows that the bound state energies increase with quantum states but decreases with the dependent mass m(x). The thermodynamics and superstatistics plots are also reported. [ABSTRACT FROM AUTHOR]

The relativistic symmetries of the Dirac equation were investigated with an energy-dependent tensor potential interaction for two different energydependent 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. [ABSTRACT FROM AUTHOR]

A solution of the radial Schrödinger equation for an improved Tietz potential function was obtained using the concept of the supersymmetric approach. The energy equation obtained for the non-relativistic wave equation was used to generate numerical values for chlorine dimer, iodine dimer and bromine dimer with the aid of their respective spectroscopic constants. The calculated results were compared with RKR values for each of the molecules. The calculated results were found to be in excellent agreement with the RKR values. [ABSTRACT FROM AUTHOR]

The solution of one-dimensional Schrödinger equation for a newly proposed potential called modified shifted Deng-Fan momentum-dependent potential is obtained via super symmetric approach. The expectation values of momentum and position were calculated using Hellmann Feynman Theorem. The effects of momentum-dependent parameter on the solutions of the system as well as the expectation values were studied. Finally, the special cases of the interacting potential were obtained. [ABSTRACT FROM AUTHOR]

The solutions of a radial Schrödinger equation are obtained for an improved generalized Pὅschl-Teller potential models. Using the supersymmetric approach, we calculated the non-relativistic energy and its corresponding un-normalized radial wave function for each potential model. Three different expectation values were calculated using Hellmann Feynman Theory (HFT) for the interacting potential model. The energy equation obtained and the various calculated expectation values were used to study NO, CH, H2 and N2 molecules. Our results showed that these molecules exhibit some similarities and some differences under the eigenvalues due to the differences in the values of the spectroscopic parameters. [ABSTRACT FROM AUTHOR]

We solved a one-dimensional time-dependent Feinberg–Horodecki equation for an improved Wei molecular energy potential function using the parametric Nikiforov–Uvarov method. The quantized momentum and the corresponding wave functions were obtained. With the help of the wave functions obtained, we calculated Shannon entropy for both the position space and momentum space. The results were used to study four molecules. The results of Shannon entropy were found to be in excellent agreement with those found in the literature. For more usefulness of these studies, the quantized momentum obtained was transformed into an energy equation with certain transformations. The energy equation was then used to calculate some thermodynamic properties such as vibrational mean energy, vibrational specific heat, vibrational mean free energy, and vibrational entropy via computation of the partition function. The thermodynamic properties studied for CO, NO, CH, and ScH showed that for a certain range of the temperature studied, the molecules exhibited similar features except for the vibrational entropy.