Analytical solutions to the Schrödinger Equation with a Combined Potential using the Series Expansion Method to Study Selected Diatomic Molecules

Abstract

Etido P. Inyang,  Joseph E.Ntibi, Olumuyiwa O.Akintola , Efiong A. Ibanga , Funmilayo Ayedun, and Eddy S.William

In this work, the Schrödinger equation with the Hulthén plus screened Kratzer Potential is solved via the series expansion method. The energy equation was used to compute the bound state energy for twelve diatomic molecules such as; CuLi, TiH, VH, TiC, HCl, LiH, H₂, ScH, CO, I₂ ,N_2, and NO  for various quantum states. Three special cases were obtained from the combined potential when some potential parameters were set to zero, resulting in Hulthén, screened Kratzer, and Kratzer potentials. To test the accuracy of our results, we computed the bound state energy eigenvalues for HCl and LiH diatomic molecules for a special case of the Kratzer and screened Kratzer potential and the results obtained were in excellent agreement with the report of other researchers in the literature.