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Dunkl–Klein–Gordon equation in higher dimensions.

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Title: Dunkl–Klein–Gordon equation in higher dimensions.
Authors: Hamil, B.1 (AUTHOR) bilel.hamil@umc.edu.dz, Lütfüoğlu, B. C.2 (AUTHOR) bekir.lutfuoglu@uhk.cz, Merad, M.3 (AUTHOR) meradm@gmail.com
Source: Modern Physics Letters A. 8/20/2025, Vol. 40 Issue 25, p1-22. 22p.
Subjects: Klein-Gordon equation, Quantum mechanics, Harmonic oscillators, Mathematics, Hypergeometric functions, Eigenfunctions, Eigenvalues, Coulomb potential
Abstract: In this study, we replace the standard partial derivatives in the Klein–Gordon equation with Dunkl derivatives and obtain exact analytical solutions for the eigenvalues and eigenfunctions of the Dunkl–Klein–Gordon equation in higher dimensions. We apply this formalism to two key quantum mechanical systems: the d-dimensional harmonic oscillator and the Coulomb potential. First, we introduce Dunkl quantum mechanics in d-dimensional hyperspherical coordinates, followed by an analysis of the d-dimensional Dunkl–Klein–Gordon oscillator. Subsequently, we derive the energy spectrum and eigenfunctions, which are expressed using confluent hypergeometric functions. Furthermore, we examine the impact of the Dunkl formalism on both the eigenvalues and eigenfunctions. In the second case, we explore both the bound-state solutions and scattering scenarios of the Dunkl–Klein–Gordon equation with the Coulomb potential. The bound-state solutions are represented in terms of confluent hypergeometric functions, while the scattering states enable us to compute the particle creation density and probability using the Bogoliubov transformation method. [ABSTRACT FROM AUTHOR]
Copyright of Modern Physics Letters A is the property of World Scientific Publishing Company 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: Dunkl–Klein–Gordon equation in higher dimensions.
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  Data: <searchLink fieldCode="AR" term="%22Hamil%2C+B%2E%22">Hamil, B.</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> bilel.hamil@umc.edu.dz</i><br /><searchLink fieldCode="AR" term="%22Lütfüoğlu%2C+B%2E+C%2E%22">Lütfüoğlu, B. C.</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> bekir.lutfuoglu@uhk.cz</i><br /><searchLink fieldCode="AR" term="%22Merad%2C+M%2E%22">Merad, M.</searchLink><relatesTo>3</relatesTo> (AUTHOR)<i> meradm@gmail.com</i>
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  Data: <searchLink fieldCode="JN" term="%22Modern+Physics+Letters+A%22">Modern Physics Letters A</searchLink>. 8/20/2025, Vol. 40 Issue 25, p1-22. 22p.
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  Data: <searchLink fieldCode="DE" term="%22Klein-Gordon+equation%22">Klein-Gordon equation</searchLink><br /><searchLink fieldCode="DE" term="%22Quantum+mechanics%22">Quantum mechanics</searchLink><br /><searchLink fieldCode="DE" term="%22Harmonic+oscillators%22">Harmonic oscillators</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematics%22">Mathematics</searchLink><br /><searchLink fieldCode="DE" term="%22Hypergeometric+functions%22">Hypergeometric functions</searchLink><br /><searchLink fieldCode="DE" term="%22Eigenfunctions%22">Eigenfunctions</searchLink><br /><searchLink fieldCode="DE" term="%22Eigenvalues%22">Eigenvalues</searchLink><br /><searchLink fieldCode="DE" term="%22Coulomb+potential%22">Coulomb potential</searchLink>
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  Label: Abstract
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  Data: In this study, we replace the standard partial derivatives in the Klein–Gordon equation with Dunkl derivatives and obtain exact analytical solutions for the eigenvalues and eigenfunctions of the Dunkl–Klein–Gordon equation in higher dimensions. We apply this formalism to two key quantum mechanical systems: the d-dimensional harmonic oscillator and the Coulomb potential. First, we introduce Dunkl quantum mechanics in d-dimensional hyperspherical coordinates, followed by an analysis of the d-dimensional Dunkl–Klein–Gordon oscillator. Subsequently, we derive the energy spectrum and eigenfunctions, which are expressed using confluent hypergeometric functions. Furthermore, we examine the impact of the Dunkl formalism on both the eigenvalues and eigenfunctions. In the second case, we explore both the bound-state solutions and scattering scenarios of the Dunkl–Klein–Gordon equation with the Coulomb potential. The bound-state solutions are represented in terms of confluent hypergeometric functions, while the scattering states enable us to compute the particle creation density and probability using the Bogoliubov transformation method. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
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  Data: <i>Copyright of Modern Physics Letters A is the property of World Scientific Publishing Company 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: 10.1142/S0217732325500944
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      – Code: eng
        Text: English
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        PageCount: 22
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      – SubjectFull: Klein-Gordon equation
        Type: general
      – SubjectFull: Quantum mechanics
        Type: general
      – SubjectFull: Harmonic oscillators
        Type: general
      – SubjectFull: Mathematics
        Type: general
      – SubjectFull: Hypergeometric functions
        Type: general
      – SubjectFull: Eigenfunctions
        Type: general
      – SubjectFull: Eigenvalues
        Type: general
      – SubjectFull: Coulomb potential
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      – TitleFull: Dunkl–Klein–Gordon equation in higher dimensions.
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            NameFull: Hamil, B.
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            NameFull: Lütfüoğlu, B. C.
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            – D: 20
              M: 08
              Text: 8/20/2025
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              Y: 2025
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