Solutions of the Schrödinger equation with Hulthén-screened Kratzer potential: Application to Diatomic Molecules

Abstract

In this study, the Schrödinger equation with the Hulthén plus screened Kratzer potentials (HSKP) are solved via the Nikiforov-Uvarov (NU) and the series expansion methods. We obtained the energy equation and the wave function in closed form with Greene-Aldrich approximation via the NU method. The series expansion method was also used to obtain the energy equation of HSKP. Three distinct cases were obtained from the combined potentials. The energy eigenvalues of HSKP for HCl, LiH, H2, and NO diatomic molecules were computed for various quantum states. To test the accuracy of our results, we computed the bound states energy of HCl and LiH, for a special case of Kratzer and screened Kratzer potentials, which are in excellent agreement with the report of other researchers.

The Effect of Topological Defect on the Mass Spectra of Heavy and Heavy-Light Quarkonia

“…The mass spectra of charmonium in the presence of TD is seen to be exactly as the ED for 1S and 2S quantum state, but in other states we noticed that they predicted results are close to the ED. As the TD was introduced by setting TD = 2 and 3, the values of the predicted masses were seen to be approaching the ED and was seen to be improved from works reported by [15,37] as shown in Table 1. For bottomonium, the mass spectra for 1S and 2S states are seen to be equal to ED.…”

“…The widely used potential is the Cornell potential (CP) which contains a Coulomb interaction term and a linear confinement term [9]. Analytically, different methods have been proposed and employed in solving the SE with a chosen potential model of interest, such as, the Asymptotic iteration method AIM [10], the Nikiforov-Uvarov (NU) method [11,12], the NU Functional Analysis (NUFA) method [13,14], the series expansion method (SEM) [15], WKB approximation method [16], exact quantization rule [17], and so on. The analytical study of heavy quark with CP has gained remarkable attention from scholars [18,19].…”

The Study of Electronic States of Ni and ScI Molecules with Screened Kratzer Potential

“…The solutions of the SE with different diatomic potential functions have been investigated by many authors [4][5][6]. Also, to obtain the SE solutions different methods have been employed such as the Asymptotic iteration method (AIM) [7], Laplace transformation method [8], supersymmetric quantum mechanics (SUSYQM) [9], the Nikiforov-Uvarov (NU) method [10][11][12][13][14][15], the Nikiforov-Uvarov-Functional Analysis (NUFA) method [16], the series expansion method (SEM) [17,18], the analytical exact iterative method (AEIM) [19], the WKB approximation method [20,21] and so on.…”

Quark-Antiquark Study with Inversely Quadratic Yukawa Potential Using the Nikiforov-Uvarov-Functional-Analysis Method

“…The Cornell potential (CP) which includes a short-range Coulomb term and a linear confinement term is generally used [4]. More so, in solving this SE with any chosen potential, an analytical method is employed, such as, the Nikiforov-Uvarov (NU) method [5][6][7][8], the NU Functional Analysis (NUFA) method [9,10], the series expansion method (SEM) [11], Laplace transformation method (LTM) [12], WKB approximation method [13], exact quantization rule [14,15], proper quantization rule [16,17], group theory approach [18] and so on [19]. The study of MS with CP has gained remarkable attention and has attracted the attention of many scholars [20][21][22][23].…”