Non-relativistic bound state solutions with α-deformed Kratzer-type potential using the super-symmetric WKB method: application to theoretic-information measures

In this work, we studied the bound states and quantum theoretic-information measurements of an α -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. Graphical abstract