Skip to main content
Log in

Photon-added coherent states for shape invariant systems

  • Regular Article
  • Published:
The European Physical Journal D Aims and scope Submit manuscript

Abstract

This paper addresses a full characterization of photon-added coherent states for shape-invariant potentials. Main properties are investigated and discussed. A statistical computation of relevant physical quantities is performed, emphasizing the importance of generalized hypergeometric functions p F q and Meijer’s G-functions for such a study.

Graphical abstract

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. E. Schrödinger, Naturwissenschaften 14, 664 (1926)

    Article  ADS  Google Scholar 

  2. J.R. Klauder, B.-S. Skagerstam, Coherent states: applications in physics and mathematical physics (World Scientific, Singapore, 1985)

  3. J.R. Klauder, Phys. Rev. D 19, 2349 (1979)

    Article  ADS  Google Scholar 

  4. A.M. Perelomov, Generalized coherent states and their applications (Springer, Berlin, 1986)

  5. S.T. Ali, J.-P. Antoine, J.-P. Gazeau, Coherent states, wavelets, and their generalizations, 2nd edn., Theoretical and mathematical physics (Springer, New York, 2014)

  6. J.-P. Gazeau, Coherent states in quantum mechanics (Wiley-VCH, Weinheim, 2009)

  7. F.A. Berezin, The method of second quantization (Nauka, Moscow, 1986)

  8. I. Aremua, J.-P. Gazeau, M.N. Hounkonnou, J. Phys. A: Math. Gen. 45, 335302 (2012)

    Article  Google Scholar 

  9. A.O. Barut, L. Girardello, Commun. Math. Phys. 21, 41 (1971)

    Article  ADS  Google Scholar 

  10. A.M. Perelomov, Commun. Math. Phys. 26, 222 (1972)

    Article  ADS  Google Scholar 

  11. R. Gilmore, Ann. Phys. (NY) 74, 391 (1972)

    Article  ADS  Google Scholar 

  12. R. Gilmore, Rev. Mex. Fis. 23, 143 (1974)

    Google Scholar 

  13. C. Aragone, G. Guerri, S. Salamó, J.L. Tanin, J. Phys. A: Math. Gen. 7, L149 (1974)

    Article  ADS  Google Scholar 

  14. N.M. Nieto, L.M. Simmons Jr., Phys. Rev. Lett. 41, 207 (1978)

    Article  ADS  Google Scholar 

  15. T. Fukui, N. Aizawa, Phys. Lett. A 189, 7 (1994)

    Article  ADS  MathSciNet  Google Scholar 

  16. A.N.F. Aleixo, A.B. Balantekin, J. Phys. A: Math. Gen. 37, 8513 (2004)

    Article  ADS  Google Scholar 

  17. E. Witten, Nucl. Phys. B 185, 5123 (1981)

    MathSciNet  Google Scholar 

  18. F. Cooper, A. Khare, U. Sukhatme, Phys. Rep. 251, 267 (1995)

    Article  ADS  MathSciNet  Google Scholar 

  19. L. Gendenshtein, JETP Lett. 38, 356 (1983)

    ADS  Google Scholar 

  20. R. Dutt, A. Khare, U. Sukhatme, Am. J. Phys. 56, 163 (1988)

    Article  ADS  Google Scholar 

  21. J. Dabrowska, A. Khare, U. Sukhatme, J. Phys. A: Math. Gen. 21, L195 (1988)

    Article  ADS  Google Scholar 

  22. V.V. Dodonov, M.A. Marchiolli, Ya.A. Korenmoy, V.I. Man’ko, Y.A. Moukhin, Phys. Rev. A 58, 4087 (1998)

    Article  ADS  Google Scholar 

  23. J.-M. Sixdeniers, K.A. Penson, J. Phys. A: Math. Gen. 34, 2859 (2001)

    Article  ADS  Google Scholar 

  24. D. Popov, J. Phys. A: Math. Gen. 35, 7205 (2002)

    Article  ADS  Google Scholar 

  25. K. Berrada, J. Math. Phys. 56, 072104 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  26. M. Daoud, Phys. Lett. A 305, 135 (2002)

    Article  ADS  MathSciNet  Google Scholar 

  27. G.S. Agarwal, K. Tara, Phys. Rev A 43, 492 (1991)

    Article  ADS  Google Scholar 

  28. G.S. Agarwal, K. Tara, Phys. Rev. A 46, 485 (1992)

    Article  ADS  Google Scholar 

  29. H.M. Li, H.C. Yuan, H.Y. Fan, Int. J. Theor. Phys. 48, 2849 (2009)

    Article  Google Scholar 

  30. J.S. Zhang, J.B. Xu, Phys. Scr. 79, 025008 (2009)

    Article  ADS  Google Scholar 

  31. V.V. Dodonov, Ya A. Korennoy, V.I. Man’ko, Y.A. Moukhin, Quantum Semiclass. Opt. 8, 413 (1996)

    Article  ADS  Google Scholar 

  32. V.V. Dodonov, J. Opt. B: Quantum Semiclass. 4, R1 (2002)

    Article  ADS  Google Scholar 

  33. V.V. Dodonov, V.I. Man’ko, Theory of nonclassical states of light (Taylor and Francis, London, 2003)

  34. M.N. Hounkonnou, E.B. Ngompe Nkouankam, J. Phys. A: Math. Theor. 42, 025206 (2009)

    Article  ADS  Google Scholar 

  35. B. Mojaveri, A. Dehghani, S. Mahmoodi, Phys. Scr. 89, 085202 (2014)

    Article  ADS  Google Scholar 

  36. B. Mojaveri, A. Dehghani, Eur. Phys. J. D 68, 315 (2014)

    Article  ADS  Google Scholar 

  37. S. Dey, V. Hussin, Phys. Rev. A 93, 053824 (2016)

    Article  ADS  Google Scholar 

  38. M. Dakna, T. Anhut, T. Opatrny, L. Knöll, D.-G. Welsch, Phys. Rev. A 55, 3184 (1997)

    Article  ADS  Google Scholar 

  39. M. Dakna, L. Knöll, D.-G. Welsch, Opt. Commun. 145, 309 (1998)

    Article  ADS  Google Scholar 

  40. M. Ban, J. Mod. Opt. 43, 1281 (1996)

    Article  ADS  Google Scholar 

  41. L. Infeld, T.E. Hull, Rev. Mod. Phys. 23, 28 (1951)

    Article  ADS  Google Scholar 

  42. O.I. Marichev, Handbook of integral transforms of higher transcendental functions: theory and algorithmic tables (Ellis Harwood, Chichester, UK, 1983)

  43. F. Oberhettinger, Tables of Mellin transforms (Springer, Berlin, 1974)

  44. A.M. Mathai, R.K. Saxena, in Generalized hypergeometric functions with applications in statistics and physical sciences, Lecture notes in mathematics (Springer, Berlin, 1973), Vol. 348

  45. K.A. Penson, A.I. Solomon, J. Math. Phys. 40, 2354 (1999)

    Article  ADS  MathSciNet  Google Scholar 

  46. L. Mandel, E. Wolf, Optical coherence and quantum optics (Cambridge University Press, Cambridge, 1995)

  47. Y.L. Luke, The special functions and their approximations (Academic Press, California, 1969)

  48. S.-H. Dong, in Factorization method in quantum mechanics (Springer, Dordrecht, 2007), Vol. 150

  49. F.W.J. Olver, Asymptotics and special functions (A K Peters, Ltd, Wellesley, 1997)

  50. http://functions.wolfram.com/HypergeometricFunctions/

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Komi Sodoga.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sodoga, K., Hounkonnou, M.N. & Aremua, I. Photon-added coherent states for shape invariant systems. Eur. Phys. J. D 72, 105 (2018). https://doi.org/10.1140/epjd/e2018-80684-y

Download citation

  • Received:

  • Revised:

  • Published:

  • DOI: https://doi.org/10.1140/epjd/e2018-80684-y

Keywords

Navigation