Skip to main content
SpringerLink
Log in

Relativistic Oscillators in Generalized Snyder Model

  • Published:
Few-Body Systems Aims and scope Submit manuscript

Abstract

We present an exact solution of one-dimensional Klein–Gordon and Dirac oscillators subjected to the uniform electric field with Snyder–de Sitter model in the momentum space, known in quantum mechanics by the stark effect. The energy eigenvalues and eigenfunctions are determined for both cases. The pure relativistic oscillator is obtained as particular case by taking the limit when the electric field vanishes. We also have determined some formulas of thermodynamics properties for relativistic oscillators within this framework.

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. H. Falomir, J. Gamboa, M. Loewe, M. Nieto, Graphene and non-Abelian quantization. J. Phys. A Math. Theor. 45, 135308 (2012)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  2. C. Quesne, Quadratic algebra approach to an exactly solvable position-dependent mass Schrödinger equation in two dimensions. SIGMA 3, 067 (2007)

    MATH  Google Scholar 

  3. I.O. Vakarchuk, G. Panochho, The effective mass of an impurity atom in the Bose liquid with a deformed Heisenberg Algebra. Ukr. J. Phys. 62, 123 (2017)

    Article  Google Scholar 

  4. A. Kempf, Uncertainty relation in quantum mechanics with quantum group symmetry. J. Math. Phys. 35, 4483 (1994)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  5. A. Kempf, G. Mangano, R.B. Mann, Hilbert space representation of the minimal length uncertainty relation. Phys. Rev. D 52, 1108 (1995)

    Article  ADS  MathSciNet  Google Scholar 

  6. S. Mignemi, Classical and quantum mechanics of the nonrelativistic Snyder model in curved space. Class. Quantum Grav. 29, 215019 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  7. S. Mignemi, R. Strajn, Quantum mechanics on a curved Snyder space. Adv. High Energy Phys. 2016, 1328284 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  8. M.M. Stetsko, Dirac oscillator and nonrelativistic Snyder–de Sitter algebra. J. Math. Phys. 56, 012101 (2015)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  9. M. Merad, M. Hadj, Moussa, Exact solution of Klein–Gordon and Dirac equations with Snyder-de Sitter algebra. J. Few-Body Syst. 59, 5 (2018). https://doi.org/10.1007/s00601-017-1326-y

    Article  ADS  Google Scholar 

  10. H.S. Snyder, Quantized space-time. Phys. Rev. 71, 38 (1947)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  11. S. Mignemi, Classical and quantum mechanics of the nonrelativistic Snyder model. Phys. Rev. D 84, 025021 (2011)

    ADS  Google Scholar 

  12. C. Leiva, Harmonic oscillator in Snyder space: the classical case and the quantum case. J. Pram. Phys. 74, 172 (2010)

    Google Scholar 

  13. C. Leiva, J. Saavedra, J.R. Villanueva, The Kepler problem in the Snyder space. J. Pram. Phys. 80, 945 (2013)

    Article  Google Scholar 

  14. C.B. Compean, M. Kirchbach, The trigonometric Rosen–Morse potential in the supersymmetric quantum mechanics and its exact solutions. J. Phys. A Math. Gen. 39, 549–552 (2005)

    MATH  Google Scholar 

  15. A.P. Raposo, H.J. Weber, D.E. Alvarez-Castillo, M. Kirchbach, Romanovski polynomials in selected physics problems. J. Centr. Eur. Phys. 5, 259–279 (2007)

    Google Scholar 

  16. M. Moshinsky, A. Szczepaniak, The dirac oscillator. J. Phys. A22, L817 (1989)

    ADS  MathSciNet  Google Scholar 

  17. D. Ito, K. Mori, E. Carriere, An example of dynamical systems with linear trajectory. Nuovo Cim. 51A, 1119 (1967)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Département des Sciences de la Matière, Faculté des Sciences Exactes, Université de Oum El Bouaghi, 04000, Oum El Bouaghi, Algeria

    M. Hadj Moussa & M. Merad

Authors
  1. M. Hadj Moussa
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Merad
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. Merad.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Hadj Moussa, M., Merad, M. Relativistic Oscillators in Generalized Snyder Model. Few-Body Syst 59, 44 (2018). https://doi.org/10.1007/s00601-018-1363-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s00601-018-1363-1

Search

Navigation