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Comments on “Barut-Girardello Coherent States for the Parabolic Cylinder Functions”

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Abstract

In Chenaghlou and Faizy (Int. J. Theor. Phys. 2008), the authors claim that they have constructed the Barut-Girardello coherent states for the parabolic cylinder functions. However, we point out here that by introducing these coherent states, Schrödinger was able to put forth the idea of “coherent states of the quantum harmonic oscillator” over eighty years ago. These coherent states are derived not only from the Barut-Girardello eigenvalue equation, but also from the Schrödinger and the Klauder-Perelomov approaches. Thus, contrary to their claim, the authors have not introduced new coherent states. In particular, a wide range of the parabolic cylinder functions do not form an orthonormal basis.

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References

  1. Chenaghlou, A., Faizy, O.: Int. J. Theor. Phys. (2008). doi:10.1007/s10773-008-9696-z

    MathSciNet  Google Scholar 

  2. Schrödinger, E.: Ann. Phys. 79(4), 361 (1926)

    Article  Google Scholar 

  3. Barut, A.O., Girardello, L.: Commun. Math. Phys. 21(1), 41 (1971)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  4. Perelomov, A.: Generalized Coherent States and Their Applications. Springer, New York (1986)

    MATH  Google Scholar 

  5. Howard, S., Roy, S.K.: Am. J. Phys. 55(12), 1109 (1987)

    Article  ADS  Google Scholar 

  6. Borzov, V.V., Damaskinsky, E.V.: J. Math. Sci. 125(2), 123 (2005)

    Article  MathSciNet  Google Scholar 

  7. Abramowitz, M., Stegun, I.A.: Handbook of Mathematical Functions: with Formulas, Graphs, and Mathematical Tables. Dover, New York (1972)

    MATH  Google Scholar 

  8. Gradshteyn, I.S., Ryzhik, I.M.: Table of Integrals, Series, and Products. Academic Press, San Diego (2000)

    MATH  Google Scholar 

  9. Haskell, T.G., Wybourne, B.G.: Proc. R. Soc. Lond. A 334, 541 (1973)

    Article  ADS  Google Scholar 

  10. Sakurai, J.J.: Modern Quantum Mechanics. Addison-Wesley, Reading (1994)

    Google Scholar 

  11. Griffiths, J.D.: Introduction to Quantum Mechanics. Prentice Hall, New York (2004)

    Google Scholar 

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Authors and Affiliations

  1. Department of Theoretical Physics and Astrophysics, Physics Faculty, University of Tabriz, P.O. Box 51666-16471, Tabriz, Iran

    H. Fakhri & A. Dehghani

  2. Department of Physics, Faculty of Science, Razi University, Kermanshah, Iran

    B. Mojaveri

Authors
  1. H. Fakhri
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  2. A. Dehghani
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  3. B. Mojaveri
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Correspondence to H. Fakhri.

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Fakhri, H., Dehghani, A. & Mojaveri, B. Comments on “Barut-Girardello Coherent States for the Parabolic Cylinder Functions”. Int J Theor Phys 48, 369–372 (2009). https://doi.org/10.1007/s10773-008-9809-8

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  • DOI: https://doi.org/10.1007/s10773-008-9809-8

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