A Quasi-Analytical Study of the Nonrelativistic Two-Center Coulomb Problem

Abstract

The Schrödinger equation with a pertaining two-center mean field potential scheme is solved by the quasi-analytical ansatz methodology. The ground-state wave function and the corresponding energy of a nonrelativistic nucleon moving in the fields of two fixed Coulomb centers are reported and the behavior of the energy vs. engaged parameters is depicted via illustrative figures.

Analytic solutions of the Schrödinger equation with non-central generalized inverse quadratic Yukawa potential

“…Physicists over the years have developed strong interest in searching for the solution of the Schrödinger equation with some potentials [1][2][3][4][5][6][7]. This is because, finding the analytical solution of the Schrödinger equation is extremely crucial in nonrelativistic quantum mechanics and the eigenfunction contains all the necessary information required to describe a quantum system under consideration.…”

Approximate solutions for diatomic molecules under combined potentials in a global monopole and Aharonov–Bohm flux field

“…Spectroscopic constants of the nine diatomic molecules have been listed in Table 1. Energy eigenvalues ÀE nl (in eV) for the diatomic molecules under the effect of KFP (4) have been recorded in Tables 2 and 3 for different values of ðn, lÞ. All the data in Tables 2 and 3 Note: Row "a" corresponds to SMKP with q e ¼ 1:0 and Z ¼ 0; Row "b" corresponds to SMKP plus HP with q e ¼ 1:0 and Z ¼ 1.…”

“…A qualitative understanding of all the important aspects of wavefunctions and energies of quantum particles can be developed by utilizing the SE of a physical system, like diatomic molecules. Over the years, numerous authors have exhibited interest in examining the SE's solutions with a variety of potential functions [1–19]. In these quantum mechanical problems, approximation procedures have been widely employed [1, 2, 4–7, 20–26] rather than exact methods [27] to find out bound state solutions of these SEs.…”

“…Over the years, numerous authors have exhibited interest in examining the SE's solutions with a variety of potential functions [1–19]. In these quantum mechanical problems, approximation procedures have been widely employed [1, 2, 4–7, 20–26] rather than exact methods [27] to find out bound state solutions of these SEs. Nikiforov–Uvarov (NU) [22, 28–33], asymptotic iteration [20, 21, 23, 34–36], Laplace transformation [37], supersymmetric quantum mechanics (SUSYQM) [38, 39] and so forth are some well‐known approximation methods for solving SEs numerically.…”