Energy eigenvalue spectra and applications of the sextic and the Coulomb perturbed potentials

Abstract

Abstract Keeping in view the importance of the anharmonic potentials, closed-form solutions to the N-dimensional Schrödinger equation, for the Coulomb perturbed and the sextic potentials using the Nikiforov-Uvarov functional analysis and power series methods respectively, are investigated. Complete energy spectrum is obtained for both the potentials by invoking some restrictions on wave function parameters of the sextic potential and the Greene-Aldrich approximation for centrifugal term of the Coulomb perturbed potential. A relationship between energy eigenvalues of the two potentials is verified in higher dimensions. This study is further extended to find physical applications of both the potentials. The energy eigenvalues of the Coulomb perturbed potential are used to compute the mass spectra of five mesons viz c c ¯ , b b ¯ , b c ¯ , c s ¯ and c q ¯ (where q = u, d). Within the framework of the sextic potential, Zr and Sn isotopic chains are analyzed and 96 Zr and 112 Sn isotopes have been identified as critical point nuclei. The results of this study are consistent with others similar studies.