Non-Relativistic Treatment of a Generalized Inverse Quadratic Yukawa Potential

Abstract

A bound state solution is a quantum state solution of a particle subjected to a potential such that the particle’s energy is less than the potential at both negative and positive infinity. The particle’s energy may also be negative as the potential approaches zero at infinity. It is characterized by the discretized eigenvalues and eigenfunctions, which contain all the necessary information regarding the quantum systems under consideration. The bound state problems need to be extended using a more precise method and approximation scheme. This study focuses on the non-relativistic bound state solutions to the generalized inverse quadratic Yukawa potential. The expression for the non-relativistic energy eigenvalues and radial eigenfunctions are derived using proper quantization rule and formula method, respectively. The results reveal that both the ground and first excited energy eigenvalues depend largely on the angular momentum numbers, screening parameters, reduced mass, and the potential depth. The energy eigenvalues, angular momentum numbers, screening parameters, reduced mass, and the potential depth or potential coupling strength determine the nature of bound state of quantum particles. The explored model is also suitable for explaining both the bound and continuum states of quantum systems.

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

“…= = = 0 then the results are in good agreement with Ref. [51]. Different ring shaped like potentials can be obtained from this new proposed Non central like potential.…”

“…It is asymptotic to a finite value as → ∞ and becomes infinite at = 0. [51] solved this potential within the framework of the proper quantization rule and eigenfunction was obtained via the Formula Method [52].The generalized inverse quadratic Yukawa potential model is of the form [51] ( ) = − 1 (1 + − ) 2 (1) [48] Compared the behaviour of the Yukawa-type potential with the Yukawa potential and the IQY potential for screening parameter values, it was noted that differences do not exist between these three potentials.…”

Arbitrary l-Solutions of the Schrodinger Equation in Arbitrary Dimensions for the Energy Dependent Generalized Inverse Quadratic Yukawa Potential

“…In our study, the energy eigenvalues of the Energy Dependent Generalized Inverse Quadratic Yukawa Potential (EDGIQYP) model were computed using (31), for different values of the energy slope parameters given( ) which are presented in Table I-IV in 3D. When = 0 , the energy equation (31) reduces to the Energy for Generalized Inverse Quadratic Yukawa Potential (EDGIQYP) model, and the corresponding numerical eigenvalues presented in Tables I-IV for = 0 agrees perfectly with the result presented in Table 1 of [18] in the absence of the energy dependence.…”

“…Comments: Equation ( 41) is the energy equation for the Inverse Quadratic Yukawa Potential in Dimensions. If = 3 , (41) reduces to the energy equation in 3D, which is identical to the results in; (37) of [42], (18) of [43] and (47) of [44].…”

“…The generalized inverse quadratic Yukawa potential (GIQYP) is a superposition of the inverse quadratic Yukawa (IQY) and the Yukawa potential. It is asymptotic to a finite value as → ∞ and becomes infinite at = 0 [18]. This potential has been solved within the framework of the Proper Quantisation Rule [19] and Eigenfunction was obtained via the Formula Method [20].…”