Skip to main content
SpringerLink
Log in

Solvability of quantum D2 model: Projection and SUSY methods

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

Abstract

We consider a 2-body particles quantum system with D2 algebra interaction and different coupling constants. Then we solve it by projection and supersymmetric methods. This work illustrates a natural way to construct algebraic and supersymmetric generalization of the other solvable Hamiltonians. This is an interesting work both in its own right and for the insights it offers in connection with the exact solvability of these models.

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

Similar content being viewed by others

References

  1. F. Calogero, J. Math. Phys. 10, 2191 (1969)

    Article  MathSciNet  ADS  Google Scholar 

  2. F. Calogero, J. Math. Phys. 10, 2197 (1969)

    Article  MathSciNet  ADS  Google Scholar 

  3. F. Calogero, J. Math. Phys. 12, 419 (1971)

    Article  MathSciNet  ADS  Google Scholar 

  4. A.P. Polychronakos, Phys. Rev. Lett. 69, 703 (1992)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  5. L. Brink, T.H. Hansson, M.A. Vasiliev, Phys. Rev. Lett. B 268, 109 (1992)

    Article  MathSciNet  ADS  Google Scholar 

  6. J.M. Leinaas, J. Myrheim, Phys. Rev. B 37, 9268 (1988)

    Article  MathSciNet  ADS  Google Scholar 

  7. F. Calogero, J. Phys. A: Math. Gen. 29, 6455 (1996)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  8. J. Wolfes, J. Math. Phys. 15, 1420 (1974)

    Article  MathSciNet  ADS  Google Scholar 

  9. F. Calogero, C. Marchiro, J. Math. Phys. 15, 1425 (1974)

    Article  ADS  Google Scholar 

  10. F.D. Buzatu, D.A. Huckaby, Physica A 299, 427 (2001)

    Article  MathSciNet  ADS  Google Scholar 

  11. D.L. Strout, D.A. Huckaby, F.Y. Wu, J. Math. Phys. 173, 60 (1991)

    MathSciNet  Google Scholar 

  12. M.A. Olshanetsky, A.M. Prelomov, Phys. Rep. 94, 313 (1983)

    Article  MathSciNet  ADS  Google Scholar 

  13. F. Calogero, J. Non-linear Math. Phys. 12, 660 (2005)

    Article  Google Scholar 

  14. A. Turbiner, L. Brink, N. Wyllard, J. Math. Phys. 39, 1285 (1998)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  15. P.K. Ghosh, A. Khare, M. Sivakumar, Phys. Rev. A 58, 821 (1998)

    Article  MathSciNet  ADS  Google Scholar 

  16. R. Floreanini, L. Lapointe, L. Vinet, Phys. Lett. B 389, 327 (1996)

    Article  MathSciNet  ADS  Google Scholar 

  17. H. Jallouli, H. Sazdjian, Ann. Phys. 253, 376 (1997)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  18. P. Mei, P. Van Isacker, Ann. Phys. 327, 1162 (2012)

    Article  ADS  MATH  Google Scholar 

  19. K. Meetz, Nuovo Cimento 34, 690 (1964)

    Article  MathSciNet  MATH  Google Scholar 

  20. H. Narnhoferz, Acta Phys. Austriaca 40, 306 (1974)

    MathSciNet  Google Scholar 

  21. E. Witten, Nucl. Phys. B 185, 513 (1981)

    Article  ADS  Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

  23. K.G. Boreskov, A. Turbiner, C.L. Vieyra, Commun. Math. Phys. 260, 17 (2005)

    Article  ADS  MATH  Google Scholar 

  24. A. Turbiner, J. Mod. Phys. Lett. A 13, 1473 (1998)

    Article  MathSciNet  ADS  Google Scholar 

  25. F. Tremblay, A. Turbiner, P. Winternitz, J. Phys. A: Math. Theor. 42, 242001 (2009)

    Article  MathSciNet  ADS  Google Scholar 

  26. A. Khare, R.K. Bhaduri, J. Phys. A 27, 2213 (1994)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  27. G. Levai, J. Phys. A 22, 689 (1989)

    Article  MathSciNet  ADS  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics, University of Guilan, 51335-1914, Rasht, Iran

    H. Panahi & H. Rahmati

Authors
  1. H. Panahi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. H. Rahmati
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to H. Panahi.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Panahi, H., Rahmati, H. Solvability of quantum D2 model: Projection and SUSY methods. Eur. Phys. J. Plus 127, 153 (2012). https://doi.org/10.1140/epjp/i2012-12153-4

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjp/i2012-12153-4

Keywords

Search

Navigation