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Bargmann transform and statistical properties for nonlinear coherent states of the isotonic oscillator

  • Ghayth Ouirdani and Othmane El Moize EMAIL logo
Published/Copyright: November 1, 2023
Zeitschrift für Naturforschung A
From the journal Zeitschrift für Naturforschung A Volume 79 Issue 1

Abstract

We construct a new class of nonlinear coherent states for the isotonic oscillator by replacing the factorial of the coefficients z n / n ! of the canonical coherent states by the factorial x n γ ! = x 1 γ . x 2 γ … x n γ with x 0 γ = 0 , where x n γ is a sequence of positive numbers and γ is a positive real parameter. This also leads to the construction of a Bargmann-type integral transform which will allow us to find some integral transforms for orthogonal polynomials. The statistics of our coherent states will also be considered by the calculus of one called Mandel parameter. The squeezing phenomenon was also discussed.

Keywords: nonlinear coherent states; isotonic oscillator; Bargmann transform; Mandel parameter
AMS Classification: 81R30; 33C45; 44A15; 46E22
Corresponding author: Othmane El Moize, Ibn Tofail University, Faculty of Sciences, Kénitra, Morocco; and The Moroccan Association of Harmonic Analysis and Spectral Geometry (AHGS), Rabat, Morocco, E-mail:

Acknowledgment

The authors would like to thank the anonymous referee for the valuable comments and suggestions. The authors also are thankful to the Moroccan Association of Harmonic Analysis and Spectral Geometry.

  1. Research ethics: Not applicable.

  2. Author contributions: The authors have accepted responsibility for the entire content of this manuscript and approved its submission.

  3. Competing interests: The authors state no conflict of interest.

  4. Research funding: None declared.

  5. Data availability: Not applicable.

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Received: 2023-07-26
Accepted: 2023-10-12
Published Online: 2023-11-01
Published in Print: 2024-01-29

© 2023 Walter de Gruyter GmbH, Berlin/Boston

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https://doi.org/10.1515/zna-2023-0206
Keywords for this article
nonlinear coherent states; isotonic oscillator; Bargmann transform; Mandel parameter

Articles in the same Issue

  1. Frontmatter
  2. Atomic, Molecular & Chemical Physics
  3. Green creation of CoFe2O4 nanosorbent for superior toxic Cd ions elimination
  4. Dynamical Systems & Nonlinear Phenomena
  5. Nonlinear vibration of microbeams subjected to a uniform magnetic field and rested on nonlinear elastic foundation
  6. Delta-shock for the Chaplygin gas Euler equations with source terms
  7. Gravitation & Cosmology
  8. Some versions of Chaplygin gas model in modified gravity framework and validity of generalized second law of thermodynamics
  9. Quantum Theory
  10. Bargmann transform and statistical properties for nonlinear coherent states of the isotonic oscillator
  11. Solid State Physics & Materials Science
  12. Low-temperature small-angle electron-electron scattering rate in Fermi metals
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