Application of Eckart-Hellmann potential to study selected diatomic molecules using Nikiforov-Uvarov-Functional analysis method

Abstract

The energy levels of the Schrödinger equation under the Eckart-Hellmann potential (EHP) energy function are studied by the Nikiforov-Uvarov-Functional Analysis (NUFA) method. We obtained the analytic solution of the energy spectra and the wave function in closed form with the help of Greene-Aldrich approximation. The numerical bound states energy for various screening parameters at different quantum states and vibrational energies of EHP for CuLi, TiH, VH, and TiC diatomic molecules were computed. Four exceptional cases of this potential were achieved. To test the accuracy of our results, we computed the bound states energy eigenvalues of Hellmann potential which are in excellent agreement with the report of other researchers.

Analyzing the effects of magnetic and Aharonov‐Bohm (AB) flux fields on the energy spectra and thermal properties of N2, NO, CO and H2 diatomic molecules

“…The solutions to the SE with a given potential give rise to the energy spectrum and wave function, which are used in many areas of physics, chemistry, mathematics, and other sciences [2]. Many researchers have recently used various analytical techniques to obtain the solutions of the SE with interacting potentials [3][4][5][6]. Examples include the series expansion method [7], WKB approximation method [8,9], asymptotic iteration method (AIM) [10,11], Nikiforov-Uvaforov (NU) method [12][13][14][15], NU-functional analysis (NUFA) approach [16], and others.…”

Masses and thermal properties of a Charmonium and Bottomonium Mesons

“…More so, in solving the SE with any potential of choice, analytical methods are employed. Most of the frequently used analytical methods are as follows, the Nikiforov-Uvarov (NU) method [6][7][8][9][10][11][12], the Nikiforov-Uvarov Functional Analysis (NUFA) method [13][14][15][16], the series expansion method (SEM) [17,18,19], Laplace transformation method (LTM) [20], Asymptoptic Iteration Method [21], WKB approximation method [22][23][24], among others [25][26][27][28][29][30][31]. The investigation of the MS with CP has gained remarkable interest, and has attracted the attention of many scholars [32][33][34][35].…”

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

“…This is because solutions of the SE contain information about the system [3]. 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.…”