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<p>In this paper, we study approximate bound state solutions of the Schrödinger equation for the new proposed non-central exponential potential as the sum of a five-parameter exponential-type potential and a ring-shaped potential, by applying the approach of supersymmetric quantum mechanics (SUSYQM) in the framework of the improved approximation scheme to the centrifugal potential. The Schrödinger equation with this model potential is separated into angular and radial components. The bound state energy eigenvalues for both the radial and angular parts of a non-relativistic equation with a new non-central model potential are derived, and the corresponding radial and angular wave functions are expressed in terms of Jacobi polynomials. We also discuss some important special cases from our model. Our results are consistent with previous studies in the literature. We also present the numerical results for the energy spectrum of some special cases of the diatomic molecules CO, NO, N<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(_{2}\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mn>2</mn> <mrow /> </mmultiscripts> </math></EquationSource> </InlineEquation> and HCL.</p>

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Approximate Bound State Solutions of the Schrödinger Equation with Combined Five-Parameter Exponential-type and Ring-Shaped Potentials by the Supersymmetry Approach

  • 期刊论文

  • 发表日期：

    2026年6月18日

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  • Bachir Kermezli,
  • Nasreddine Zaghou

摘要

In this paper, we study approximate bound state solutions of the Schrödinger equation for the new proposed non-central exponential potential as the sum of a five-parameter exponential-type potential and a ring-shaped potential, by applying the approach of supersymmetric quantum mechanics (SUSYQM) in the framework of the improved approximation scheme to the centrifugal potential. The Schrödinger equation with this model potential is separated into angular and radial components. The bound state energy eigenvalues for both the radial and angular parts of a non-relativistic equation with a new non-central model potential are derived, and the corresponding radial and angular wave functions are expressed in terms of Jacobi polynomials. We also discuss some important special cases from our model. Our results are consistent with previous studies in the literature. We also present the numerical results for the energy spectrum of some special cases of the diatomic molecules CO, NO, N \(_{2}\) 2 and HCL.