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A unified scheme of central symmetric shape-invariant potentials.

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Title: A unified scheme of central symmetric shape-invariant potentials.
Authors: Koohrokhi, T1 (AUTHOR) t.koohrokhi@gu.ac.ir, Izadpanah, A1 (AUTHOR), Gerayloo, M1 (AUTHOR)
Source: Pramana: Journal of Physics. Dec2024, Vol. 98 Issue 4, p1-14. 14p.
Subjects: Coulomb potential, Conserved quantity, Pseudopotential method, Dynamical systems, Harmonic oscillators
Abstract: Most physical systems, whether classical or quantum mechanical, exhibit spherical symmetry. Angular momentum, denoted as ℓ , is a conserved quantity that appears in the centrifugal potential when a particle moves under the influence of a central force. This study introduces a formalism in which ℓ plays a unifying role, consolidating solvable central potentials into a superpotential. This framework illustrates that the Coulomb potential emerges as a direct consequence of a homogeneous (r-independent) isotropic superpotential. Conversely, an ℓ -independent central superpotential results in a 3-dimensional harmonic oscillator (3-DHO) potential. Moreover, a local ℓ -dependent central superpotential generates potentials applicable to finite-range interactions such as molecular or nucleonic systems. Additionally, we discuss generalisations to arbitrary D dimensions and investigate the properties of the superpotential to determine when supersymmetry is broken or unbroken. This scheme also shows that the free-particle wave function in three dimensions is obtained from the spontaneous breakdown of supersymmetry and clarifies how a positive 3-DHO potential, as an upside-down potential, can have a negative energy spectrum. We also present complex isospectral deformations of the central superpotential and superpartners, which can have interesting applications for open systems in dynamic equilibrium. Finally, as a practical application, we apply this formalism to specify a new effective potential for the deuteron. [ABSTRACT FROM AUTHOR]
Copyright of Pramana: Journal of Physics is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: A unified scheme of central symmetric shape-invariant potentials.
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  Data: <searchLink fieldCode="AR" term="%22Koohrokhi%2C+T%22">Koohrokhi, T</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> t.koohrokhi@gu.ac.ir</i><br /><searchLink fieldCode="AR" term="%22Izadpanah%2C+A%22">Izadpanah, A</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Gerayloo%2C+M%22">Gerayloo, M</searchLink><relatesTo>1</relatesTo> (AUTHOR)
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  Data: <searchLink fieldCode="JN" term="%22Pramana%3A+Journal+of+Physics%22">Pramana: Journal of Physics</searchLink>. Dec2024, Vol. 98 Issue 4, p1-14. 14p.
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  Data: <searchLink fieldCode="DE" term="%22Coulomb+potential%22">Coulomb potential</searchLink><br /><searchLink fieldCode="DE" term="%22Conserved+quantity%22">Conserved quantity</searchLink><br /><searchLink fieldCode="DE" term="%22Pseudopotential+method%22">Pseudopotential method</searchLink><br /><searchLink fieldCode="DE" term="%22Dynamical+systems%22">Dynamical systems</searchLink><br /><searchLink fieldCode="DE" term="%22Harmonic+oscillators%22">Harmonic oscillators</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: Most physical systems, whether classical or quantum mechanical, exhibit spherical symmetry. Angular momentum, denoted as ℓ , is a conserved quantity that appears in the centrifugal potential when a particle moves under the influence of a central force. This study introduces a formalism in which ℓ plays a unifying role, consolidating solvable central potentials into a superpotential. This framework illustrates that the Coulomb potential emerges as a direct consequence of a homogeneous (r-independent) isotropic superpotential. Conversely, an ℓ -independent central superpotential results in a 3-dimensional harmonic oscillator (3-DHO) potential. Moreover, a local ℓ -dependent central superpotential generates potentials applicable to finite-range interactions such as molecular or nucleonic systems. Additionally, we discuss generalisations to arbitrary D dimensions and investigate the properties of the superpotential to determine when supersymmetry is broken or unbroken. This scheme also shows that the free-particle wave function in three dimensions is obtained from the spontaneous breakdown of supersymmetry and clarifies how a positive 3-DHO potential, as an upside-down potential, can have a negative energy spectrum. We also present complex isospectral deformations of the central superpotential and superpartners, which can have interesting applications for open systems in dynamic equilibrium. Finally, as a practical application, we apply this formalism to specify a new effective potential for the deuteron. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Pramana: Journal of Physics is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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      – Type: doi
        Value: 10.1007/s12043-024-02824-0
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      – Code: eng
        Text: English
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        PageCount: 14
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    Subjects:
      – SubjectFull: Coulomb potential
        Type: general
      – SubjectFull: Conserved quantity
        Type: general
      – SubjectFull: Pseudopotential method
        Type: general
      – SubjectFull: Dynamical systems
        Type: general
      – SubjectFull: Harmonic oscillators
        Type: general
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      – TitleFull: A unified scheme of central symmetric shape-invariant potentials.
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            NameFull: Izadpanah, A
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            – D: 01
              M: 12
              Text: Dec2024
              Type: published
              Y: 2024
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              Value: 98
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