Investigating of Singularity of Central Shape Invariant Potentials

Document Type : Full length research Paper

Authors

Department of Physics, Faculty of Sciences, Golestan University, Gorgan, Iran

Abstract

In this research, the singularity of the central shape-invariant potentials, which have a singularity of the inverse-square power , has been investigated. It has been shown that in quantum mechanics, for , the eigenvalue problem is well-defined and, as a result, the energy spectrum can be determined. In the transition region, for , both regular and irregular wave functions are square integrable and therefore acceptable, but the boundary conditions for determining the eigenvalues and eigenfunctions are not sufficient and there is no a specific predetermined mechanism for choosing a linear combination of wave functions. For , the particle is drawn to the singularity, and therefore, there is no any ground state with finite energy. It has also been shown using supersymmetric quantum mechanics that the inverse-square potential is the result of the singular inverse superpotential . Supersymmetric quantum mechanics provides a mechanism that, without any additional constraints, the less singular wave function is chosen and the potential is placed in the transition region for .

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References

 
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Journal of Research on Many-body Systems
Volume 13, Issue 4 - Serial Number 39
Winter 2024
March 2024
Pages 57-68

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History

  • Receive Date: 24 May 2023
  • Revise Date: 02 October 2023
  • Accept Date: 02 December 2023

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