Eigensolutions of the Schrödinger equation with a class of Yukawa potentials via supersymmetric approach

Abstract

Using the basic concept of the supersymmetric shape invariance approach and formalism, we obtained an approximate solution of the Schrödinger equation with an interaction of inversely quadratic Yukawa potential, Yukawa potential and Coulomb potential which we considered as a class of Yukawa potentials. By varying the potential strengths, we obtained a solution for Hellmann potential, Yukawa potential, Coulomb potential and inversely quadratic Yukawa potential. The numerical results we obtained show that the interaction of these potentials is equivalent to each of the potential.

Bound state solutions of the Schrödinger equation with energy-dependent molecular Kratzer potential via asymptotic iteration method

“…The solution of the Schrödinger equation contains all the necessary information needed for the full description of a quantum state such as the probability density and entropy of the system 7,8 . The Schrödinger equation with many physical potentials model have been investigated in recent times with different advance mathematical technique such as Nikiforov-Uvarov (NU) method [9][10][11] , asymptotic iteration method (AIM) [12][13][14][15][16] , functional analysis approach 16 , supersymmetric quantum mechanics (SUSYQM) [17][18][19][20] among others 21 . One of such potential models is the Kratzer potential 22 where D is the dissociation energy and a is the equilibrium internuclear length.…”

Relativistic treatment of the Hellmann-generalized morse potential

“…Some of the techniques devised to investigate these potentials are; Asymptotic Iteration Method (AIM) [5,13,19], Nikiforov-Uvarov (NU) method [20,21], shape invariant supersymmetry (SUSYQM) [22], Modified factorization method (MFM) [23], Formula method [24], Exact quantization rule [25][26][27], Factorization method [28] and others.…”

A study of thermodynamic properties of quadratic exponential-type potential in D-dimensions

“…Different methods employed over the years in obtaining these solutions include Nikiforov-Uvarov (NU) method [9][10][11][12], Supersymmetry quantum mechanics (SUSYQM) [13][14][15][16], Asymptotic iteration methos (AIM) [17], Proper and exact quantization rule [18][19], Factorization method [20], Functional Analysis Approach FAA (also known here as Modified Factorization Method) [21], etc. The modified factorization method is usually used to transform a secondorder homogeneous linear differential equation into a hypergeometric equation, with the help of a transformation scheme [22].…”