Exact energy spectrum of the generalized Dirac oscillator in an electric field

  • H. P. Laba
  • V. M. Tkachuk
Regular Article


We study the generalized (1 + 1) -dimensional Dirac oscillator in a nonuniform electric field. It is shown that in the case of a specially chosen electric field the eigenvalue equation can be cast in the form of supersymmetric quantum mechanics. This gives the possibility to find the exact solution of the energy spectrum of the generalized Dirac oscillator in a nonuniform electric field. Explicit examples of exact solutions are presented. We show that a sufficiently large electric field destroys the bounded eigenstates.


  1. 1.
    D. Ito, K. Mori, E. Carrieri, Nuovo Cimento A 51, 1119 (1967)ADSCrossRefGoogle Scholar
  2. 2.
    M. Moshinsky, A. Szczepaniak, J. Phys. A 22, L817 (1989)ADSCrossRefGoogle Scholar
  3. 3.
    J.A. Franco-Villafane, E. Sadurn, S. Barkhofen, U. Kuhl, F. Mortessagne, T.H. Seligman, Phys. Rev. Lett. 111, 170405 (2013)ADSCrossRefGoogle Scholar
  4. 4.
    C. Quesne, J. Phys. A 50, 081001 (2017)ADSCrossRefGoogle Scholar
  5. 5.
    C. Quesne, V.M. Tkachuk, J. Phys. A 38, 1747 (2005)ADSMathSciNetCrossRefGoogle Scholar
  6. 6.
    C. Quesne, V.M. Tkachuk, J. Phys. A 39, 10909 (2006)ADSMathSciNetCrossRefGoogle Scholar
  7. 7.
    Choon-Lin Hoa, Pinaki Roy, Ann. Phys. 312, 161 (2004)ADSCrossRefGoogle Scholar
  8. 8.
    Sameer M. Ikhdair, J. Mod. Phys. 3, 170 (2012)CrossRefGoogle Scholar
  9. 9.
    D. Dutta, O. Panella, P. Roy, Ann. Phys. 331, 120 (2013)ADSCrossRefGoogle Scholar
  10. 10.
    Georg Junker, Akira Inomata, Path Integral and Spectral Representations for Supersymmetric Dirac-Hamiltonians, arXiv:1712.08759Google Scholar
  11. 11.
    Fred Cooper, Avinash Khare, Uday Sukhatme, Phys. Rep. 251, 267 (1995)ADSMathSciNetCrossRefGoogle Scholar
  12. 12.
    Asim Gangopadhyaya, Jeffry V. Mallow, Constantin Rasinariu, Supersymmetric Quantum Mechanics: An Introduction (World Scientific, 2011)Google Scholar
  13. 13.
    L.E. Gendenshtein, JETP Lett. 38, 356 (1983)ADSGoogle Scholar
  14. 14.
    V.M. Tkachuk, S.I. Vakarchuk, Phys. Lett. A 228, 141 (1997)ADSMathSciNetCrossRefGoogle Scholar
  15. 15.
    D. Natha, P. Roy, Ann. Phys. 351, 13 (2014)ADSCrossRefGoogle Scholar

Copyright information

© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Applied Physics and Nanomaterials ScienceLviv Polytechnic National UniversityLvivUkraine
  2. 2.Department for Theoretical PhysicsIvan Franko National University of LvivLvivUkraine

Personalised recommendations