Study of bound states for diatomic molecules by resolution of Schrödinger equation with pseudo-harmonic and Mie potentials via Nikiforov–Uvarov (NU) method

Abstract

Atomic physicists have faced the challenge of solving the Schrödinger equation for a system composed of [Formula: see text] electrons that experience both the attractive Coulomb force from the nucleus and the repulsive Coulomb force between each pair of electrons. The resolution of the Schrödinger equation and finding the bound states and the eigenfunctions of the mentioned equation are resolved by using many different methods, both analytically and numerically, with generalized pseudo-harmonics and the Mie potential. The eigenvalues and corresponding eigenfunctions of the Schrödinger equation with pseudo-harmonics and the Mie potential are obtained with the Nikiforov–Uvarov method. The two potentials are a combination of at least two terms. In this work, the method of approximation that is used for solving secular equations is that of Nikiforov and Uvarov, which is mentioned above, and we applied it to the Schrödinger equation to obtain some of the first eigenvalues of the quantum mechanical system. After comparing the eigenvalues results with other earlier works, the method gave satisfactory solutions, as expected.