Approximate Analytical Solution of the Yukawa Potential with Arbitrary Angular Momenta

Abstract

The Yukawa potential is often used to compute bound-state normalizations and energy levels of neutral atoms. By using the generalized parametric Nikiforov-Uvarov method, we obtain approximate analytical solutions of the radial Schrödinger equation for the Yukawa potential. The energy eigenvalues and the corresponding eigenfunctions are calculated in closed forms. Some numerical results are presented and show that these results are in good agreement with those obtained previously by other methods. Also, we find the energy levels of the familiar pure Coulomb potential energy levels when the screening parameter of the Yukawa potential goes to zero.

Approximate Analytical Solutions of the Perturbed Yukawa Potential with Centrifugal Barrier

“…Same as in Table 2, buth = 2µ = 1, a = 0.2 fm −1 , and n = 0. which is identical to (30) of [34,35]. Also, when V 1 = 0, potential (1) reduces to the standard Yukawa potential [22,23] and its energy levels can be obtained from (21) as…”

“…under the physical condition n + l + 1 ≤ µV 0 /a [22]. When the screening parameter a approaches zero, the standard Yukawa potential reduces to a Coulomb potential.…”

Nonrelativistic Studies of Diatomic Molecules of Schrödinger Particles with Yukawa Plus Ring-Shaped Potential Model

“…Noncentral potential in particular has been studied in various fields of nuclear physics and quantum chemistry which could be used for the interaction between deformed pair of nuclei and ring shaped molecules like benzenes [1][2][3][4][5]. Yukawa potential is one of the short ranged potentials that have been studied in physics, they have Coulombic behavior for small r and are exponentially damped for large r , and they have limited number of bound states characterized by the presence of the screening parameter α [6][7][8][9][10]. This model receives great attention for it plays an important role in high energy and particle physics, atomic physics, chemical physics, gravitational plasma physics and solid state physics.…”

Yukawa-angle Dependent Potential and its Applications to Diatomic Molecules under Schrodinger wave Equation

“…Yukawa potential is one of the short ranged potentials that have been studied in physics, they have coulombic behavior for small r and are exponentially damped for large r , and they have limited number of bound states characterized by the presence of the screening parameter α [6][7][8][9][10]. This model receives great attention due to the fact that it plays an important role in high energy and particle physics, atomic physics, chemical physics, gravitational plasma physics and solid state physics.…”