Skip to main content
SpringerLink
Log in

Coherent states of the two-dimensional non-separable supersymmetric Morse potential

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

Abstract

Supersymmetry is a fundamental feature of a quantum theory described by a supersymmetric Hamiltonian comprised of several quantum mechanical Hamiltonians with different potentials that allows us to relate information about the states and spectra of the constituent Hamiltonians. In this paper we reconstruct Ioffe’s set of states for the singular non-separable two-dimensional Morse potential using supersymmetry from a non-degenerate set of states constructed for the initial separable Morse Hamiltonian. We define generalised coherent states, compute their uncertainty relations, and we find that the singularity in the partner Hamiltonian significantly affects the localisation of the coherent state wavefunction.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

References

  1. E. Witten, Nucl. Phys. B 188, 513 (1981)

    Article  ADS  Google Scholar 

  2. E. Witten, J. Differ. Geom. 17, 661 (1982)

    Article  Google Scholar 

  3. C.B. Compean, M. Kirchbach, J. Phys. A Math. Gen. 39, 547 (2005)

    Article  ADS  Google Scholar 

  4. S. Domínguez-Hernández, D.J. Fernández C., Int. J. Theor. 50, 1993 (2011)

    Article  Google Scholar 

  5. D.J. Fernández C., V.S. Morales-Salgado, J. Phys. Conf. Ser. 512, 12 (2014)

    Google Scholar 

  6. D.J. Fernández C., V.S. Morales-Salgado, Ann. Phys. 388, 122 (2018)

    Article  ADS  Google Scholar 

  7. D.J. Fernández C., V. Hussin, V.S. Morales-Salgado, Eur. Phys. J. Plus 134, 18 (2019)

    Article  Google Scholar 

  8. I. Marquette, SIGMA 8, 063 (2012)

    MathSciNet  Google Scholar 

  9. M.-A. Fiset, V. Hussin, J. Phys. Conf. Ser. 624, 012016 (2015)

    Article  Google Scholar 

  10. A. Das, S. Okubo, S.A. Pernice, Mod. Phys. Lett. A 12, 581 (1997)

    Article  ADS  Google Scholar 

  11. M.V. Ioffe, D.N. Nishnianidze, Phys. Rev. A 76, 052114 (2007)

    Article  ADS  MathSciNet  Google Scholar 

  12. P.M. Morse, Phys. Rev. 34, 57 (1929)

    Article  ADS  Google Scholar 

  13. W.E. Smyser, D.J. Wilson, J. Chem. Phys. 50, 182 (1969)

    Article  ADS  Google Scholar 

  14. J.P. Chesick, J. Chem. Phys. 49, 3772 (1968)

    Article  ADS  Google Scholar 

  15. P.F. Endres, J. Chem. Phys. 47, 798 (1967)

    Article  ADS  Google Scholar 

  16. A. Bordoni, N. Manini, Int. J. Quantum Chem. 107, 782 (2007)

    Article  ADS  Google Scholar 

  17. J.C. Rode et al., 2D Mater. 6, 015021 (2018)

    Article  Google Scholar 

  18. Z. Zali, A. Amani, J. Sadeghi, B. Pourhassan, Phys. B Condens. Matter 614, 413045 (2021)

    Article  Google Scholar 

  19. T. Begušić, J. Vaníček, J. Chem. Phys. 153, 024105 (2020)

    Article  Google Scholar 

  20. C. Quesne, Int. J. Mod. Phys. B 27, 1250073 (2012)

    Article  ADS  Google Scholar 

  21. R.J. Glauber, Phys. Rev. 131, 2766 (1963)

    Article  ADS  MathSciNet  Google Scholar 

  22. E.C.G. Sudarshan, Phys. Rev. Lett. 10, 277 (1963)

    Article  ADS  MathSciNet  Google Scholar 

  23. J.P. Gazeau, Coherent states in quantum physics (Wiley, 2009)

  24. J. Moran, V. Hussin, Quantum rep. 1, 260 (2019)

    Article  Google Scholar 

  25. J. Moran & V. Hussin, quantum theory and symmetries: proceedings of the 11th international symposium (2021)

  26. J. Moran, V. Hussin, I. Marquette, J. Phys. A Math. Theor. 54, 275301 (2021)

    Article  Google Scholar 

  27. M. Angelova, V. Hussin, J. Phys. A Math. Theor. 41, 304016 (2008)

    Article  Google Scholar 

  28. J. Moran, Eur. Phys. J. Plus 136, 716 (2021)

    Article  Google Scholar 

  29. R.F. Fox, M.H. Choi, Phys. Rev. A 64, 042104 (2001)

    Article  ADS  Google Scholar 

  30. M. Ioffe, J.M. Guilarte, P. Valinevich, Ann. Phys. 321, 2552 (2006)

    Article  ADS  Google Scholar 

  31. M.V. Ioffe, J. Phys. A Math. Gen. 37, 10363 (2004)

    Article  ADS  Google Scholar 

  32. M.V. Ioffe, P.A. Valinevich, J. Phys. A Math. Gen. 38, 2497 (2005)

    Article  ADS  Google Scholar 

  33. A. Das, S.A. Pernice, Nucl. Phys. B 561, 357 (1999)

    Article  ADS  Google Scholar 

  34. P. Panigrahi, U.P. Sukhatme, Phys. Lett. A 178, 251 (1993)

    Article  ADS  MathSciNet  Google Scholar 

  35. V. Hussin, I. Marquette, SIGMA 7, 024 (2011)

    Google Scholar 

  36. E.F. de Lima, J.E.M. Hornos, J. Chem. Phys. 125, 164110 (2006)

    Article  ADS  Google Scholar 

  37. W. Gao-Feng, C. Wen-Li, Chin. Phys. B 19, 6 (2010)

    Article  Google Scholar 

  38. P. Zhang, arXiv:1010.3820 (2010)

  39. S.-H. Dong, Factorization method in quantum mechanics, fundamental theories of physics, vol. 150 (Springer, Dordrecht, 2007)

    Book  Google Scholar 

  40. J.R. Klauder, J. Phys. A Math. Gen. 29, L293 (1996)

    Article  ADS  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  42. H. Kwon, K.C. Tan, T. Volkoff, H. Jeong, Phys. Rev. Lett. 122, 040503 (2019)

    Article  ADS  Google Scholar 

  43. K. Zelaya, O. Rosas-Ortiz, Z. Blanco-Garcia, S. Cruz, Y. Cruz, Adv. Math. Phys. 2017, 7168592 (2017)

    Article  Google Scholar 

  44. A. Hertz, N.J. Cerf, S. De Bièvre, Phys. Rev. A 102, 032413 (2020)

    Article  ADS  Google Scholar 

  45. C.M. Caves, Phys. Rev. D 23, 1693 (1981)

    Article  ADS  Google Scholar 

  46. J. Abadie et al., Nat. Phys. 7, 962 (2011)

    Article  Google Scholar 

  47. Y.-Q. Li, P. Lynam, M. Xiao, P.J. Edwards, Phys. Rev. Lett. 78, 3105 (1997)

    Article  ADS  Google Scholar 

  48. D. Li, Y. Yao, Sci. Rep. 11, 7785 (2021)

    Article  ADS  Google Scholar 

  49. L. Duan, Nat. Photon. 13, 73 (2019)

    Article  ADS  Google Scholar 

  50. M. Pavšič, Int. J. Geom. Methods Mod. Phys. 13, 1630015 (2016)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

J. Moran acknowledges the support of the Département de physique at the Université de Montréal. V. Hussin acknowledges the support of research grants from NSERC of Canada. Both authors would like to thank I. Marquette for his help in the preparation of this paper.

Author information

Authors and Affiliations

  1. Département de Physique, Université de Montréal, Montréal, QC, H3C 3J7, Canada

    James Moran

  2. Centre de Recherches Mathématiques, Université de Montréal, Montréal, QC, H3C 3J7, Canada

    James Moran & Véronique Hussin

  3. Département de Mathématiques et de Statistique, Université de Montréal, Montréal, QC, H3C 3J7, Canada

    Véronique Hussin

Authors
  1. James Moran
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Véronique Hussin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to James Moran.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Moran, J., Hussin, V. Coherent states of the two-dimensional non-separable supersymmetric Morse potential. Eur. Phys. J. Plus 136, 1096 (2021). https://doi.org/10.1140/epjp/s13360-021-02096-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjp/s13360-021-02096-2

Search

Navigation