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

Abstract 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. With the aid of the DSO, the percentage average absolute deviation (PAAD) of computed data from the experimental data of the 7Li2 (2 3Πg), NaBr (X 1Σ+), KBr (X 1Σ+) and KRb (B 1Π) molecules are 1.3319%, 0.2108%, 0.2359% and 0.8841%, respectively. The PAAD values obtained by employing the equations of molar entropy, scaled molar enthalpy, scaled molar Gibbs free energy and isobaric molar heat capacity are 1.2919%, 1.5639%, 1.5957% and 2.4041%, respectively, from the experimental data of the KBr (X 1Σ+) molecule. The results for the potential energies, bound-state energy spectra, and thermodynamic functions are in good agreement with the literature on diatomic molecules

Non-relativistic bound state solutions with

In this work, we studied the bound states and quantum theoretic-information measurements of an $$\alpha$$-deformed Kratzer-type potential with the Schrodinger equation. The ground state wave function in position-momentum spaces and the energy spectra equations for arbitrary quantum numbers are obtained in closed-form via the super-symmetric WKB method and Fourier transform. The obtained energy equation is bounded and reduces to the molecular Kratzer-type energy and the hydrogenic Coulomb’s energy upon proper adjustment of potential parameters. The wave function was used to obtain the Fisher, Shannon, Rényi and Tsallis theoretic-information measures numerically. Our results for the information measures obey the local Fisher inequality and the Bialynicki-Birula–Mycielski inequality. The Rényi and Tsallis entropies in position-momentum spaces were obtained for the index number $$q = 0.5$$ and $$q = 2$$ as a function of the potential parameter. The results of the theoretic-information quantities and probability densities revealed that the potential parameters strongly influence the localization and delocalization of the position of a nano particle

Information-theoretic measures and thermodynamic properties under magnetic and Aharonov–Bohm flux fields

We investigated the effects of external magnetic and Aharonov–Bohm flux fields on the thermodynamic properties, Fisher, Shannon and Rényi information-theoretic measures using the non-relativistic Schrödinger equation with a Varshni-type potential. We adopted the parametric Nikiforov–Uvarov approach to obtain the analytical bound states in closed form. The thermodynamic functions such as the free energy, specific heat capacity, vibrational entropy and mean energy were analyzed. Also, the results for the 2D Fisher's information-theoretic measure obey the inequality $$I\left(\rho \right)I\left(\gamma \right)\ge 16$$. The Rényi entropies sum applied to lithium hydride (LiH) diatomic molecule obeys the inequality $${R}_{2}\left(\rho \right)$$+$${R}_{2/3}\left(\gamma \right)\ge$$ 4.19926 for 2D system. Also, the global Shannon entropies sum inequality for the LiH molecule is verified. The applications of the external fields were found to strongly influence the splitting of the energy overlaps, the thermodynamic functions and the information-theoretic measures. The results may aid the understanding of the dynamics of quantum particles and molecules in external fields