Solvability of quantum D2 model: Projection and SUSY methods

Regular Article

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.

Keywords

Jacobi Polynomial Angular Part SUSY Partner Exact Solvability Supersymmetric Generalization 

References

  1. 1.
    F. Calogero, J. Math. Phys. 10, 2191 (1969)MathSciNetCrossRefADSGoogle Scholar
  2. 2.
    F. Calogero, J. Math. Phys. 10, 2197 (1969)MathSciNetCrossRefADSGoogle Scholar
  3. 3.
    F. Calogero, J. Math. Phys. 12, 419 (1971)MathSciNetADSCrossRefGoogle Scholar
  4. 4.
    A.P. Polychronakos, Phys. Rev. Lett. 69, 703 (1992)MathSciNetADSCrossRefMATHGoogle Scholar
  5. 5.
    L. Brink, T.H. Hansson, M.A. Vasiliev, Phys. Rev. Lett. B 268, 109 (1992)MathSciNetADSCrossRefGoogle Scholar
  6. 6.
    J.M. Leinaas, J. Myrheim, Phys. Rev. B 37, 9268 (1988)MathSciNetADSCrossRefGoogle Scholar
  7. 7.
    F. Calogero, J. Phys. A: Math. Gen. 29, 6455 (1996)MathSciNetADSCrossRefMATHGoogle Scholar
  8. 8.
    J. Wolfes, J. Math. Phys. 15, 1420 (1974)MathSciNetADSCrossRefGoogle Scholar
  9. 9.
    F. Calogero, C. Marchiro, J. Math. Phys. 15, 1425 (1974)ADSCrossRefGoogle Scholar
  10. 10.
    F.D. Buzatu, D.A. Huckaby, Physica A 299, 427 (2001)MathSciNetADSCrossRefGoogle Scholar
  11. 11.
    D.L. Strout, D.A. Huckaby, F.Y. Wu, J. Math. Phys. 173, 60 (1991)MathSciNetGoogle Scholar
  12. 12.
    M.A. Olshanetsky, A.M. Prelomov, Phys. Rep. 94, 313 (1983)MathSciNetADSCrossRefGoogle Scholar
  13. 13.
    F. Calogero, J. Non-linear Math. Phys. 12, 660 (2005)CrossRefGoogle Scholar
  14. 14.
    A. Turbiner, L. Brink, N. Wyllard, J. Math. Phys. 39, 1285 (1998)MathSciNetADSCrossRefMATHGoogle Scholar
  15. 15.
    P.K. Ghosh, A. Khare, M. Sivakumar, Phys. Rev. A 58, 821 (1998)MathSciNetADSCrossRefGoogle Scholar
  16. 16.
    R. Floreanini, L. Lapointe, L. Vinet, Phys. Lett. B 389, 327 (1996)MathSciNetADSCrossRefGoogle Scholar
  17. 17.
    H. Jallouli, H. Sazdjian, Ann. Phys. 253, 376 (1997)MathSciNetADSCrossRefMATHGoogle Scholar
  18. 18.
    P. Mei, P. Van Isacker, Ann. Phys. 327, 1162 (2012)ADSCrossRefMATHGoogle Scholar
  19. 19.
    K. Meetz, Nuovo Cimento 34, 690 (1964)MathSciNetCrossRefMATHGoogle Scholar
  20. 20.
    H. Narnhoferz, Acta Phys. Austriaca 40, 306 (1974)MathSciNetGoogle Scholar
  21. 21.
    E. Witten, Nucl. Phys. B 185, 513 (1981)ADSCrossRefGoogle Scholar
  22. 22.
    F. Cooper, A. Khare, U. Sukhatme, Phys. Rep. 251, 267 (1995)MathSciNetADSCrossRefGoogle Scholar
  23. 23.
    K.G. Boreskov, A. Turbiner, C.L. Vieyra, Commun. Math. Phys. 260, 17 (2005)ADSCrossRefMATHGoogle Scholar
  24. 24.
    A. Turbiner, J. Mod. Phys. Lett. A 13, 1473 (1998)MathSciNetADSCrossRefGoogle Scholar
  25. 25.
    F. Tremblay, A. Turbiner, P. Winternitz, J. Phys. A: Math. Theor. 42, 242001 (2009)MathSciNetADSCrossRefGoogle Scholar
  26. 26.
    A. Khare, R.K. Bhaduri, J. Phys. A 27, 2213 (1994)MathSciNetADSCrossRefMATHGoogle Scholar
  27. 27.
    G. Levai, J. Phys. A 22, 689 (1989)MathSciNetADSCrossRefMATHGoogle Scholar

Copyright information

© Società Italiana di Fisica and Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Department of PhysicsUniversity of GuilanRashtIran

Personalised recommendations