Study of a bounded Coulomb potential

Abstract

In this paper, we have studied a new bounded Coulombic potential for the Schrödinger equation with the asymptotic iteration method (AIM). We have calculated energy eigenvalues for different potential parameters.

On the energies of a bounded Coulomb potential

“…We clearly appreciate that V (r ) tends to zero when R → ∞, except at the singular points r = 0 and r = R. This fact explains why the energy calculated by those authors approaches zero from above as shown in their table 1. As R increases, the model approaches a free particle, which is not consistent with the authors' statement: It is obvious that when R → ∞, the potential becomes Coulombic [1]. In fact, the authors obtained negative energies only when B/R is sufficiently large as in their table 4.…”

“…We show the present eigenvalues in table 1 as a benchmark for future applications of other methods. They are certainly more accurate than the AIM eigenvalues [1] displayed in the third column.…”

“…It is not clear how it can describe, for example, the interaction of a pair of particles within a box because in such a case we would face difficulties when trying to separate the motion of the center of mass from the relative one [3,4]. Unfortunately, the authors did not provide precise details about the application they had in mind [1], and for this reason we cannot discuss the utility of the model any further.…”

“…Quite recently, Ateser et al [1] proposed a bounded Coulomb potential for the study of quarks confined in a hadron. This potential confines a particle to a box of radius R and, according to the authors, it behaves as a Coulomb potential when R → ∞.…”

“…The purpose of this paper is to discuss the model proposed by Ateser et al [1] and contrast their AIM results with the RPM ones. In section 2, we discuss the model and some of the solutions obtained by those authors.…”